Substitution Method
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Question 1 of 18
1. Question
Solve the following simultaneous equations by substitution.`x-y=8``2x+y=1`-
`x=` (3)`y=` (-5)
Hint
Help VideoCorrect
Great Work!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`x-y` `=` `8` Equation `1` `2x+y` `=` `1` Equation `2` Next, solve for `x` in Equation `1`.`x-y` `=` `8` `x-y``+y` `=` `8``+y` Add `y` to both sides `x` `=` `8+y` Simplify Substitute `x` into Equation `2`.`2``x``+y` `=` `1` Equation `2` `2``(8+y)``+y` `=` `1` `x=8+y` `16+2y+y` `=` `1` Distribute `2` inside the parenthesis `16+3y` `=` `1` Simplify `16+3y``-16` `=` `1``-16` Solve for `y` `3y` `=` `-15` `y` `=` `-5` Divide both sides by `3` Now, substitute the value of `y` into Equation `1``x-``y` `=` `8` Equation `1` `x-``(-5)` `=` `8` `y=-5` `x+5` `=` `8` `x+5``-5` `=` `8``-5` Simplify `x` `=` `3` `x=3, y =-5` -
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Question 2 of 18
2. Question
Solve the following simultaneous equations by substitution.`2x-y=6``x+3y=10`-
`x=` (4)`y=` (2)
Hint
Help VideoCorrect
Correct!
Incorrect
Help VideoThe substitution method removes one of the variables by replacement in a pair of simultaneous equations.First, label the two equations `1` and `2` respectively.`2x-y` `=` `6` Equation `1` `x+3y` `=` `10` Equation `2` Next, solve for `y` in Equation `1`.`2x-y` `=` `6` `2x-y``+y-6` `=` `6``+y-6` Add `y-6` to both sides `2x-6` `=` `y` Simplify `y` `=` `2x-6` Simplify Substitute `y` into Equation `2`.`x+3``y` `=` `10` Equation `2` `x+3``(2x-6)` `=` `10` `y=2x-6` `x+6x-18` `=` `10` Distribute `3` inside the parenthesis `7x-18` `=` `10` Simplify `7x-18``+18` `=` `10``+18` Solve for `x` `7x` `=` `28` `x` `=` `4` Divide both sides by `7` Now, substitute the value of `x` into Equation `1``2``x``-y` `=` `6` Equation `1` `2``(4)``-y` `=` `6` `x=4` `8-y` `=` `6` `8-y``-8` `=` `6``-8` Simplify `-y` `=` `-2` `y` `=` `2` `x=4, y =2` -
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Question 3 of 18
3. Question
Solve the following simultaneous equations by substitution.`2a+b=5``5a-3b=7`-
`a=` (2)`b=` (1)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Help VideoThe substitution method removes one of the variables by replacement in a pair of simultaneous equations.First, label the two equations `1` and `2` respectively.`2a+b` `=` `5` Equation `1` `5a-3b` `=` `7` Equation `2` Next, solve for `b` in Equation `1`.`2a+b` `=` `5` `2a+b``-2a` `=` `5``-2a` Subtract `2a` from both sides `b` `=` `5-2a` Simplify Substitute `b` into Equation `2`.`5a-3``b` `=` `7` Equation `2` `5a-3``(5-2a)` `=` `7` `b=5-2a` `5a-15+6a` `=` `7` Distribute `-3` inside the parenthesis `11a-15` `=` `7` Simplify `11a-15``+15` `=` `7``+15` Solve for `a` `11a` `=` `22` `a` `=` `2` Divide both sides by `11` Now, substitute the value of `a` into Equation `1``2``a``+b` `=` `5` Equation `1` `2``(2)``+b` `=` `5` `a=2` `4+b` `=` `5` `4+b``-4` `=` `5``-4` Simplify `b` `=` `1` `a=2, b=1` -
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Question 4 of 18
4. Question
Solve the following simultaneous equations by substitution.`2x+y=1``x-y=2`-
`x=` (1)`y=` (-1)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Help VideoThe substitution method removes one of the variables by replacement in a pair of simultaneous equations.First, label the two equations `1` and `2` respectively.`2x+y` `=` `1` Equation `1` `x-y` `=` `2` Equation `2` Next, solve for `x` in Equation `2`.`x-y` `=` `2` `x-y``+y` `=` `2``+y` Add `y` to both sides of the equation `x` `=` `2+y` Simplify Substitute `x` into Equation `1`.`2``x``+y` `=` `1` Equation `1` `2``(2+y)``+y` `=` `1` `x=2+y` `4+2y+y` `=` `1` Distribute `2` inside the parenthesis `4+3y` `=` `1` Simplify `4+3y``-4` `=` `1``-4` Solve for `y` `3y` `=` `-3` `y` `=` `-1` Divide both sides by `3` Now, substitute the value of `y` into Equation `2``x-``y` `=` `2` Equation `2` `x-``(-1)` `=` `2` `y=-1` `x+1` `=` `2` `x+1``-1` `=` `2``-1` Simplify `x` `=` `1` `x=1, y=-1` -
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Question 5 of 18
5. Question
Solve the following simultaneous equations by substitution.`x-y=1``2x+y=11`-
`x=` (4)`y=` (3)
Hint
Help VideoCorrect
Great Work!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`x-y` `=` `1` Equation `1` `2x+y` `=` `11` Equation `2` Next, solve for `x` in Equation `1`.`x-y` `=` `1` `x-y` `+y` `=` `1` `+y` Add `y` to both sides `x` `=` `1+y` Simplify Substitute `x` into Equation `2`.`2``x``+y` `=` `11` Equation `2` `2``(1+y)``+y` `=` `11` `x=1+y` `2y+2+y` `=` `11` Distribute `2` inside the parenthesis `3y+2` `=` `11` Simplify `3y+2` `-2` `=` `11` `-2` Solve for `y` `3y` `=` `9` `3y` `div3` `=` `9` `div3` Divide both sides by `3` `y` `=` `3` Now, substitute the value of `y` into Equation `1``x-``y` `=` `1` Equation `1` `x-``(3)` `=` `1` `y=3` `x-3` `+3` `=` `1` `+3` Add `3` to both sides `x` `=` `4` `x=4, y =3` -
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Question 6 of 18
6. Question
Solve the following simultaneous equations by substitution.`2x+y=7``4x-2y=10`-
`x=` (3)`y=` (1)
Hint
Help VideoCorrect
Correct!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`2x+y` `=` `7` Equation `1` `4x-2y` `=` `10` Equation `2` Next, solve for `y` in Equation `1`.`2x+y` `=` `7` `2x+y` `-2x` `=` `7` `-2x` Subtract `2x` from both sides `y` `=` `7-2x` Simplify Substitute `y` into Equation `2`.`4x-2` `y` `=` `10` Equation `2` `4x-2` `(7-2x)` `=` `11` `y=7-2x` `4x-14+4x` `=` `10` Distribute `2` inside the parenthesis `8x-14` `=` `10` Simplify `8x-14` `+14` `=` `10` `+14` Solve for `x` `8x` `=` `24` `8x` `div8` `=` `24` `div8` Divide both sides by `8` `x` `=` `3` Now, substitute the value of `x` into Equation `1``2``x``+y` `=` `7` Equation `1` `2``(3)``+y` `=` `7` `x=3` `6+y` `-6` `=` `7` `-6` Subtract `6` from both sides `y` `=` `1` Check our workTo check if the values of `x` and `y` are correct, substitute both values to the first equation`2x+y` `=` `7` `2(3)+1` `=` `7` Substitute `x=3` and `y=1` `6+1` `=` `7` `7` `=` `7` This proves that the values of `x` and `y` are correct.`x=3, y=1` -
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Question 7 of 18
7. Question
Solve the following simultaneous equations by substitution.`a-3b=2``2a-b=14`-
`a=` (8)`b=` (2)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`a-3b` `=` `2` Equation `1` `2a-b` `=` `14` Equation `2` Next, solve for `a` in Equation `1`.`a-3b` `=` `2` `a-3b` `+3b` `=` `2` `+3b` Add `3b` to both sides `a` `=` `2+3b` Simplify Substitute `a` into Equation `2`.`2``a` `-b` `=` `14` Equation `2` `2``(2+3b)` `-b` `=` `14` `a=2+3b` `4+6b-b` `=` `14` Distribute `2` inside the parenthesis `5b+4` `=` `14` Simplify `5b+4` `-4` `=` `14` `-4` Solve for `b` `5b` `=` `10` `5b` `div5` `=` `10` `div5` Divide both sides by `5` `b` `=` `2` Now, substitute the value of `b` into Equation `1``a-3``b` `=` `2` Equation `1` `a-3``(2)` `=` `2` `b=2` `a-6` `+6` `=` `2` `+6` Add `6` to both sides `a` `=` `8` `a=8, b=2` -
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Question 8 of 18
8. Question
Solve the following simultaneous equations by substitution.`3x-2y=20``x+2y=-4`-
`x=` (4)`y=` (-4)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`3x-2y` `=` `20` Equation `1` `x+2y` `=` `-4` Equation `2` Next, solve for `x` in Equation `2`.`x+2y` `=` `-4` `x+2y` `-2y` `=` `-4` `-2y` Subtract `2y` from both sides `x` `=` `-4-2y` Simplify Substitute `x` into Equation `1`.`3``x` `-2y` `=` `20` Equation `1` `3``(-4-2y)` `-2y` `=` `20` `x=-4-2y` `-12-6y-2y` `=` `20` Distribute `3` inside the parenthesis `-12-8y` `=` `20` Simplify `-12-8y` `+12` `=` `20` `+12` Solve for `y` `-8y` `=` `32` `-8y` `div(-8)` `=` `32` `div(-8)` Divide both sides by `-8` `y` `=` `-4` Now, substitute the value of `y` into Equation `2``x+2``y` `=` `-4` Equation `2` `x+2``(-2)` `=` `-4` `y=-2` `x-8` `+8` `=` `-4` `+8` Add `8` to both sides `x` `=` `4` `x=4, y=-4` -
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Question 9 of 18
9. Question
Solve the following simultaneous equations by substitution.`2x+5y=7``x-y=7`-
`x=` (6)`y=` (-1)
Hint
Help VideoCorrect
Excellent!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
Substitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`2x+5y` `=` `7` Equation `1` `x-y` `=` `7` Equation `2` Next, solve for `x` in Equation `2`.`x-y` `=` `7` `x-y` `+y` `=` `7` `+y` Add `y` from both sides `x` `=` `7+y` Simplify Substitute `x` into Equation `1`.`2``x` `+5y` `=` `7` Equation `1` `2``(7+y)` `+5y` `=` `7` `x=7+y` `14+2y+5y` `=` `7` Distribute `2` inside the parenthesis `14+7y` `=` `7` Simplify `14+7y` `-14` `=` `7` `-14` Solve for `y` `7y` `=` `-7` `7y` `div7` `=` `-7` `div7` Divide both sides by `7` `y` `=` `-1` Now, substitute the value of `y` into Equation `2``x-` `y` `=` `7` Equation `2` `x-` `(-1)` `=` `7` `y=-2` `x+1` `=` `7` Simplify `x+1` `-1` `=` `7` `-1` Subtract `1` from both sides `x` `=` `6` `x=6, y=-1` -
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Question 10 of 18
10. Question
Solve the following simultaneous equations by substitution.`a-b=5``2a+b=4`-
`a=` (3)`b=` (-2)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`a-b` `=` `5` Equation `1` `2a+b` `=` `4` Equation `2` Next, solve for `a` in Equation `1`.`a-b` `=` `5` `a-b` `+b` `=` `5` `+b` Add `b` to both sides `a` `=` `5+b` Simplify Substitute `a` into Equation `2`.`2``a` `+b` `=` `4` Equation `2` `2``(5+b)` `+b` `=` `4` `a=5+b` `10+2b+b` `=` `4` Distribute `2` inside the parenthesis `10+3b` `=` `4` Simplify `10+3b` `-10` `=` `4` `-10` Solve for `b` `3b` `=` `-6` `3b` `div3` `=` `-6` `div3` Divide both sides by `3` `b` `=` `-2` Now, substitute the value of `b` into Equation `1``a-` `b` `=` `5` Equation `1` `a-` `(-2)` `=` `5` `b=2` `a+2` `=` `5` Simplify `a+2` `-2` `=` `5` `-2` Subtract `2` from both sides `a` `=` `3` `a=3, b=-2` -
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Question 11 of 18
11. Question
Solve the following simultaneous equations by substitution.`b=2a+2``2a+5b=10`-
`a=` (0)`b=` (2)
Hint
Help VideoCorrect
Well Done!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`b` `=` `2a+2` Equation `1` `2a+5b` `=` `10` Equation `2` Next, substitute `b` from Equation `1` into Equation `2`.`2a+5``b` `=` `10` Equation `2` `2a+5``(2a+2)` `=` `10` `b=2a+2` `2a+10a+10` `=` `10` Distribute `5` inside the parenthesis `12a+10` `=` `10` Simplify `12a+10` `-10` `=` `10` `-10` Solve for `a` `12a` `=` `0` `12a` `div12` `=` `0` `div12` Divide both sides by `12` `a` `=` `0` Now, substitute the value of `a` into Equation `1``b` `=` `2``a``+2` Equation `1` `b` `=` `2``(0)``+2` `a=0` `b` `=` `0+2` `b` `=` `2` `a=0, b=2` -
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Question 12 of 18
12. Question
Solve the following simultaneous equations by substitution.`2m+5n=5``m-5n=10`-
`m=` (5)`n=` (-1)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`2m+5n` `=` `5` Equation `1` `m-5n` `=` `10` Equation `2` Next, solve for `m` in Equation `2`.`m-5n` `=` `10` `m-5n` `+5n` `=` `10` `+5n` Add `5n` to both sides `m` `=` `10+5n` Simplify Substitute `m` into Equation `1`.`2``m` `+5n` `=` `5` Equation `1` `2``(10+5n)` `+5n` `=` `5` `m=10+5n` `20+10n+5n` `=` `5` Distribute `2` inside the parenthesis `20+15n` `=` `5` Simplify `20+15n` `-20` `=` `5` `-20` Solve for `n` `15n` `=` `-15` `15n` `div15` `=` `-15` `div15` Divide both sides by `15` `n` `=` `-1` Now, substitute the value of `n` into Equation `2``m-5``n` `=` `10` Equation `1` `m-5``(-1)` `=` `10` `n=-1` `m+5` `-5` `=` `10` `-5` Subtract `5` from both sides `m` `=` `5` `m=5, n=-1` -
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Question 13 of 18
13. Question
Solve the following simultaneous equations by substitution.`8a+5b=6``4a+2b=4`-
`a=` (2)`b=` (-2)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`8a+5b` `=` `6` Equation `1` `4a+2b` `=` `4` Equation `2` Next, solve for `b` in Equation `2`.`4a+2b` `=` `4` `(4a``div2``)+(2b``div2``)` `=` `4``div2` Divide the values of both sides by `2` `2a+b` `-2a` `=` `2` `-2a` Subtract `2a` from both sides `b` `=` `2-2a` Simplify Substitute `b` into Equation `1`.`8a+5``b` `=` `6` Equation `1` `8a+5``(2-2a)` `=` `6` `b=2-2a` `8a+10-10a` `=` `6` Distribute `5` inside the parenthesis `10-2a` `=` `6` Simplify `10-2a` `-10` `=` `6` `-10` Solve for `a` `-2a` `=` `-4` `-2a` `div(-2)` `=` `-4` `div(-2)` Divide both sides by `-2` `a` `=` `2` Now, substitute the value of `a` into Equation `2``4``a` `+2b` `=` `4` Equation `1` `4``(2)` `+2b` `=` `4` `a=2` `8+2b` `-8` `=` `4` `-8` Subtract `8` from both sides `2b``div2` `=` `-4``div2` Divide both sides by `2` `b` `=` `-2` `a=2, b=-2` -
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Question 14 of 18
14. Question
Solve the following simultaneous equations by substitution.`2x+5y=17``3x+3y=12`-
`x=` (1)`y=` (3)
Hint
Help VideoCorrect
Excellent!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`2x+5y` `=` `17` Equation `1` `3x+3y` `=` `12` Equation `2` Next, solve for `x` in Equation `2`.`3x+3y` `=` `12` `(3x``div3``)+(3y``div3``)` `=` `12``div3` Divide the values of both sides by `3` `x+y` `-y` `=` `4` `-y` Subtract `y` from both sides `x` `=` `4-y` Simplify Substitute `x` into Equation `1`.`2``x` `+5y` `=` `17` Equation `1` `2``(4-y)` `+5y` `=` `17` `x=4-y` `8-2y+5y` `=` `17` Distribute `2` inside the parenthesis `8+3y` `=` `17` Simplify `8+3y` `-8` `=` `17` `-8` Solve for `y` `3y` `=` `9` `3y` `div3` `=` `9` `div3` Divide both sides by `3` `y` `=` `3` Now, substitute the value of `y` into Equation `2``3x+3``y` `=` `12` Equation `2` `3x+3``(3)` `=` `12` `y=3` `3x+9` `-9` `=` `12` `-9` Subtract `9` to both sides `3x` `div3` `=` `3` `div3` Divide both sides by `3` `x` `=` `1` `x=1, y=3` -
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Question 15 of 18
15. Question
Solve the following simultaneous equations by substitution.`3x+7y=4``2x+3y=1`-
`x=` (-1)`y=` (1)
Hint
Help VideoCorrect
Correct!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`3x+7y` `=` `4` Equation `1` `2x+3y` `=` `1` Equation `2` Next, solve for `x` in Equation `2`.`2x+3y` `=` `1` `2x+3y` `-3y` `=` `1``-3y` Subtract `3y` from both sides `2x` `div2` `=` `(1-3y)` `div2` Divide both sides by `2` `x` `=` `(1-3y)/2` Simplify Substitute `x` into Equation `1`.`3``x` `+7y` `=` `4` Equation `1` `3``((1-3y)/2)` `+7y` `=` `4` `x=(1-3y)/2` $$\left(3\left(\frac{1-3y}{2}\right)\color{#CC0000}{\times2}\right)+(7y\color{#CC0000}{\times2})$$ `=` `4``times2` Multiply all values by `2` `3(1-3y)+14y` `=` `8` `3-9y+14y` `=` `8` Distribute `3` inside the parenthesis `3+5y` `=` `8` Simplify `3+5y` `-3` `=` `8` `-3` Solve for `y` `5y` `=` `5` `5y` `div5` `=` `5` `div5` Divide both sides by `5` `y` `=` `1` Now, substitute the value of `y` into Equation `2``2x+3``y` `=` `1` Equation `2` `2x+3``(1)` `=` `1` `y=1` `2x+3` `-3` `=` `1` `-3` Subtract `3` from both sides `2x` `div2` `=` `-2` `div2` Divide both sides by `2` `x` `=` `-1` `x=-1, y=1` -
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Question 16 of 18
16. Question
Solve the following simultaneous equations by substitution.`5a+2b=4``2a-3b=13`-
`a=` (2)`b=` (-3)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`5a+2b` `=` `4` Equation `1` `2a-3b` `=` `13` Equation `2` Next, solve for `a` in Equation `2`.`2a-3b` `=` `13` `2a-3b` `+3b` `=` `13``+3b` Add `3b` to both sides `2a` `div2` `=` `(13+3b)` `div2` Divide both sides by `2` `a` `=` `(13+3b)/2` Simplify Substitute `a` into Equation `1`.`5``a` `+2b` `=` `4` Equation `1` `5``((13+3b)/2)` `+2b` `=` `4` `a=(13+3b)/2` $$\left(5\left(\frac{13+3b}{2}\right)\color{#CC0000}{\times2}\right)+(2b\color{#CC0000}{\times2})$$ `=` `4``times2` Multiply all values by `2` `5(13+3b)+4b` `=` `8` `65+15b+4b` `=` `8` Distribute `5` inside the parenthesis `65+19b` `=` `8` Simplify `65+19b` `-65` `=` `8` `-65` Solve for `b` `19b` `=` `-57` `19b` `div19` `=` `-57` `div19` Divide both sides by `19` `b` `=` `-3` Now, substitute the value of `b` into Equation `2``2a-3``b` `=` `13` Equation `2` `2a-3``(-3)` `=` `13` `b=-3` `2a+9` `-9` `=` `13` `-9` Subtract `9` from both sides `2a` `div2` `=` `4` `div2` Divide both sides by `2` `a` `=` `2` `a=2, b=-3` -
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Question 17 of 18
17. Question
Solve the following simultaneous equations by substitution.`4x-5y=14``2x+3y=-4`-
`x=` (1)`y=` (-2)
Hint
Help VideoCorrect
Great Work!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`4x-5y` `=` `14` Equation `1` `2x+3y` `=` `-4` Equation `2` Next, solve for `x` in Equation `2`.`2x+3y` `=` `-4` `2x+3y` `-3y` `=` `-4``-3y` Subtract `3y` from both sides `2x` `div2` `=` `(-4-3y)` `div2` Divide both sides by `2` `x` `=` `(-4-3y)/2` Simplify Substitute `x` into Equation `1`.`4``x` `-5y` `=` `14` Equation `1` `4``((-4-3y)/2)` `-5y` `=` `14` `x=(-4-3y)/2` $$\left(4\left(\frac{-4-3y}{2}\right)\color{#CC0000}{\times2}\right)-(5y\color{#CC0000}{\times2})$$ `=` `14``times2` Multiply all values by `2` `4(-4-3y)-10y` `=` `28` `-16-12y-10y` `=` `28` Distribute `4` inside the parenthesis `-16-22y` `=` `28` Simplify `-16-22y` `+16` `=` `28` `+16` Solve for `y` `-22y` `=` `44` `-22y` `div-22` `=` `44` `div-22` Divide both sides by `-22` `y` `=` `-2` Now, substitute the value of `y` into Equation `2``2x+3``y` `=` `-4` Equation `2` `2x+3``(-2)` `=` `-4` `y=-2` `2x-6` `+6` `=` `-4` `+6` Add `6` to both sides `2x` `div2` `=` `2` `div2` Divide both sides by `2` `x` `=` `1` `x=1, y=-2` -
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Question 18 of 18
18. Question
Solve the following simultaneous equations by substitution.`7x-2y=6``3x+4y=22`-
`x=` (2)`y=` (4)
Hint
Help VideoCorrect
Well Done!
Incorrect
Help VideoSubstitution Method
- `1)` make one variable the subject
- `2)` substitute into second equation
- `3)` solve the second equation
- `4)` substitute back
First, label the two equations `1` and `2` respectively.`7x-2y` `=` `6` Equation `1` `3x+4y` `=` `22` Equation `2` Next, solve for `y` in Equation `1`.`7x-2y` `=` `6` `7x-2y` `+2y` `=` `6` `+2y` Add `2y` to both sides `7x` `-6` `=` `6+2y` `-6` Subtract `2y` from both sides `(7x-6)` `div2` `=` `2y` `div2` Divide both sides by `2` `(7x-6)/2` `=` `y` Simplify `y` `=` `(7x-6)/2` Simplify Substitute `y` into Equation `2`.`3x+4``y` `=` `22` Equation `2` `3x+4``((7x-6)/2)` `=` `22` `y=(7x-6)/2` $$(3x\color{#CC0000}{\times2})+\left(4\left(\frac{7x-6}{2}\right)\color{#CC0000}{\times2}\right)$$ `=` `22``times2` Multiply all values by `2` `6x+4(7x-6)` `=` `44` `6x+28x-24` `=` `44` Distribute `4` inside the parenthesis `34x-24` `=` `44` Simplify `34x-24` `+24` `=` `44` `+24` Solve for `x` `34x` `=` `68` `34x` `div34` `=` `68` `div34` Divide both sides by `34` `x` `=` `2` Now, substitute the value of `x` into Equation `1``7``x` `-2y` `=` `6` Equation `1` `7``(2)` `-2y` `=` `6` `x=2` `14-2y` `-14` `=` `6` `-14` Subtract `14` from both sides `-2y` `div-2` `=` `-8` `div-2` Divide both sides by `-2` `y` `=` `4` `x=2, y=4` -
Quizzes
- Mean, Mode, Median and Range
- Create Frequency Tables & Graphs
- Interpret Frequency Tables
- Create and Interpret Bar Graphs (Histograms)
- Create and Interpret Line Graphs (Frequency Polygon)
- Interpret Cumulative Frequency Tables and Charts
- Create Grouped Frequency Tables and Graphs
- Interpret Grouped Frequency Tables
- Create and Interpret Dot Plots (Line Plots)
- Finding the Interquartile Range
- Create and Interpret Box & Whisker Plots
- Create and Interpret Stem & Leaf Plots
- Arithmetic Sequences
- Geometric Sequences
- Plotting Points
- Table of Values
- Equations of a Line
- Finding Intersection Points
- Solve Quadratics by Factoring
- The Quadratic Formula
- Completing the Square
- Intro to Quadratic Functions (Parabolas)
- Graph Quadratic Functions in Standard Form
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Graph Quadratic Functions using the Discriminant
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities
- Convert To and From Scientific Notation
- Multiply & Divide in Scientific Notation
- Scientific Notation Word Problems
- Simplify Radicals
- Simplify Radicals with Variables
- Add and Subtract Radicals
- Multiply Radicals
- Divide Radicals
- Multiply and Divide Radicals with Variables
- Simplify Radicals using the Distributive Property
- Rationalizing The Denominator
- Relative and Absolute Maxima and Minima
- Digit Word Problems
- Measurement Word Problems
- Money Word Problems
- Age Word Problems
- Probability Word Problems
- Geometry Word Problems
- Proportion Word Problems
- Digit Word Problems
- Measurement Word Problems
- Money Word Problems
- Age Word Problems
- Probability Word Problems
- Geometry Word Problems
- Proportion Word Problems
- Circumference of Circles
- Area of Circles
- Simplify Radicals
- Simplify Radicals with Variables
- Add and Subtract Radicals
- Multiply Radicals
- Divide Radicals
- Multiply and Divide Radicals with Variables
- Simplify Radicals using the Distributive Property
- Rationalizing The Denominator
- Arithmetic Sequences
- Arithmetic Series (Sum)
- Arithmetic Sequence Problems
- Geometric Sequences
- Geometric Series (Sum)
- Geometric Sequence Problems
- Infinite Geometric Series
- Sigma Notation (Summation)
- Recurring Decimals
- Arithmetic Sequences
- Arithmetic Series (Sum)
- Arithmetic Sequence Problems
- Geometric Sequences
- Geometric Series (Sum)
- Geometric Sequence Problems
- Infinite Geometric Series
- Sigma Notation (Summation)
- Recurring Decimals
- Substitution Method
- Elimination Method
- Systems of Nonlinear Equations
- Systems of Equations Word Problems
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Substitution Method
- Elimination Method
- Systems of Nonlinear Equations
- Systems of Equations Word Problems
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Circumference of Circles
- Area of Circles
- Area of Sectors (Basic)
- Radians and Arc Length (Radians)
- Area of Sectors and Segments (Radians)
- Write an Equation from Circle Graphs
- Graph Circles in Standard Form
- Graph Circles in Expanded Form
- Determine Similar Figures
- Solve Similar Figures
- Simplify Trigonometric Identities
- Factor Trigonometric Identities
- Trigonometric Identity Proofs
- Simplify Trigonometric Identities
- Factor Trigonometric Identities
- Trigonometric Identity Proofs
- Correlation
- Line of Best Fit
- Least Squares Regression
- Median Regression Line
- Limits
- Perimeter of Basic Shapes
- Perimeter of Advanced Shapes
- Perimeter of Composite Shapes
- Perimeter Word Problems
- Perimeter of Basic Shapes
- Perimeter of Advanced Shapes
- Perimeter of Composite Shapes
- Perimeter Word Problems
- Absolute Value Equations
- Absolute Value Inequalities
- Absolute Value Equations
- Absolute Value Inequalities
- Multiply Binomials
- Multiply Binomials – FOIL Method
- FOIL Method – Same First Variable
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Difference of Two Squares (Longer Expressions)
- Great Circle Distances
- Add to or Subtract Time from a Time and Date
- Time Difference and Longitudes
- International Time Zones
- Time and Travelling Word Problems
- Multiplying Polynomials 3 Terms
- Division of Polynomials
- Remainder Theorem
- Factor Theorem
- Graphing Polynomials
- Distance Between Two Points
- Midpoint of a Line
- Slope of a Line
- Slope Intercept Form: Graph an Equation
- Slope Intercept Form: Write an Equation
- Determine if a Point Lies on a Line
- Graph Linear Inequalities
- Convert Standard Form and Slope Intercept Form
- Point Slope Form
- Parallel Lines
- Perpendicular Lines
- Solve a System of Equations by Graphing
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Slope of a Line 1
- Slope of a Line 2
- Slope Intercept Form: Graph an Equation 1
- Slope Intercept Form: Graph an Equation 2
- Slope Intercept Form: Write an Equation 1
- Graph Linear Inequalities 2
- Convert Standard Form and Slope Intercept Form 1
- Convert Standard Form and Slope Intercept Form 2
- Point Slope Form 1
- Point Slope Form 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2
- Graph Linear Inequalities 1
- Find Mean, Mode, Median and Range 1
- Find Mean, Mode, Median and Range 2
- Find Mean, Mode, Median and Range 3
- Create Frequency Tables & Graphs
- Interpret Frequency Tables 1
- Interpret Frequency Tables 2
- Create and Interpret Bar & Line Graphs (Histograms)
- Interpret Cumulative Frequency Tables and Charts 1
- Interpret Cumulative Frequency Tables and Charts 2
- Create Grouped Frequency Tables and Graphs
- Interpret Grouped Frequency Tables
- Create and Interpret Dot Plots (Line Plots) 1
- Create and Interpret Dot Plots (Line Plots) 2
- Finding the Interquartile Range 1
- Finding the Interquartile Range 2
- Create and Interpret Box & Whisker Plots 1
- Create and Interpret Box & Whisker Plots 2
- Create and Interpret Box & Whisker Plots 3
- Create and Interpret Box & Whisker Plots 4
- Create and Interpret Stem & Leaf Plots 1
- Create and Interpret Stem & Leaf Plots 2
- Create and Interpret Stem & Leaf Plots 3
- Create and Interpret Stem & Leaf Plots 4
- Simple Probability 1
- Simple Probability 2
- Simple Probability 3
- Simple Probability 4
- Complementary Probability 1
- Compound Events 1
- Compound Events 2
- Venn Diagrams (Non Mutually Exclusive)
- Independent Events 1
- Independent Events 2
- Dependent Events (Conditional Probability)
- Probability Tree (Independent)
- Probability Tree (Dependent)
- Convert Between Percentages, Fractions and Decimals 1
- Convert Between Percentages, Fractions and Decimals 2
- Convert Between Percentages, Fractions and Decimals 3
- Convert Between Percentages, Fractions and Decimals 4
- Graph Quadratic Functions using the Discriminant
- Percent from a Graph (Visual) 1
- Percent from a Graph (Visual) 2
- Percent from a Graph (Visual) 3
- Convert Between Percentages, Fractions and Decimals 1
- Convert Between Percentages, Fractions and Decimals 2
- Convert Between Percentages, Fractions and Decimals 3
- Convert Between Percentages, Fractions and Decimals 4
- Convert Mixed Numbers, Mixed Fractions and Fraction Percentages 1
- Convert Mixed Numbers, Mixed Fractions and Fraction Percentages 2
- Percent of an Amount 1
- Percent of an Amount 2
- Increase and Decrease an Amount by a Percent
- Increase and Decrease an Amount by a Percent – Word Problems 1
- Increase and Decrease an Amount by a Percent – Word Problems 2
- Increase and Decrease an Amount by a Percent – Word Problems 3
- Percent of Change
- Percent of Change – Word Problems
- Percent of an Amount – Word Problems 1
- Percent of an Amount – Word Problems 2
- Percent of an Amount – Word Problems 3
- Find Base from Percent of an Amount (Unitary Method) 1
- Find Base from Percent of an Amount (Unitary Method) 2
- One Amount as a Percentage of Another Amount
- Find Original Amount Before Percent Change (Unitary Method)
- Depreciation
- Percent from a Graph (Visual) 1
- Percent from a Graph (Visual) 2
- Percent from a Graph (Visual) 3
- Convert Between Percentages, Fractions and Decimals 1
- Convert Between Percentages, Fractions and Decimals 2
- Convert Between Percentages, Fractions and Decimals 3
- Convert Between Percentages, Fractions and Decimals 4
- Convert Mixed Numbers, Mixed Fractions and Fraction Percentages 1
- Convert Mixed Numbers, Mixed Fractions and Fraction Percentages 2
- Percent of an Amount 1
- Percent of an Amount 2
- Increase and Decrease an Amount by a Percent
- Increase and Decrease an Amount by a Percent – Word Problems 1
- Increase and Decrease an Amount by a Percent – Word Problems 2
- Increase and Decrease an Amount by a Percent – Word Problems 3
- Percent of Change
- Percent of Change – Word Problems
- Percent of an Amount – Word Problems 1
- Percent of an Amount – Word Problems 2
- Percent of an Amount – Word Problems 3
- Find Base from Percent of an Amount (Unitary Method) 1
- Find Base from Percent of an Amount (Unitary Method) 2
- One Amount as a Percentage of Another Amount
- Find Original Amount Before Percent Change (Unitary Method)
- Depreciation
- Shaded Fractions 1
- Shaded Fractions 2
- Equivalent Fractions 1
- Equivalent Fractions 2
- Equivalent Fractions 3
- Equivalent Fractions 4
- Simplify Fractions 1
- Simplify Fractions 2
- Simplify Fractions 3
- Find the LCM
- Comparing Fractions 1
- Comparing Fractions 2
- Comparing Fractions 3
- Mixed and Improper Fractions 1
- Mixed and Improper Fractions 2
- Mixed and Improper Fractions 3
- Add and Subtract Fractions 1
- Add and Subtract Fractions 2
- Add and Subtract Fractions 3
- Add and Subtract Fractions 4
- Multiply and Divide Fractions 1
- Multiply and Divide Fractions 2
- Multiply and Divide Fractions 3
- Add and Subtract Mixed Numbers 1
- Add and Subtract Mixed Numbers 2
- Add and Subtract Mixed Numbers 3
- Multiply and Divide Mixed Fractions 1
- Multiply and Divide Mixed Fractions 2
- Multiply and Divide Mixed Fractions 3
- Multiply and Divide Mixed Fractions 4
- Fraction Word Problems: Addition and Subtraction 1
- Fraction Word Problems: Addition and Subtraction 2
- Fraction Word Problems: Addition and Subtraction 3
- Fraction Word Problems: Addition and Subtraction 4
- Fraction Word Problems: Multiplication and Division
- Find the Fraction of a Quantity
- Find the Quantity of a Quantity 1
- Find the Quantity of a Quantity 2
- Find the Fraction of a Quantity: Word Problems 1
- Find the Fraction of a Quantity: Word Problems 2
- Find the Fraction of a Quantity: Word Problems 3
- Find the Fraction of a Quantity: Word Problems 4
- Find the Quantity of a Quantity: Word Problems
- Order of Operations Involving Fractions 1
- Order of Operations Involving Fractions 2
- Add and Subtract Negative Numbers on the Number Line 1
- Add and Subtract Negative Numbers on the Number Line 2
- Add and Subtract Negative Numbers on the Number Line 3
- Add and Subtract Negative Numbers on the Number Line 4
- Add and Subtract Negative Numbers 1
- Add and Subtract Negative Numbers 2
- Add and Subtract Negative Numbers 3
- Add and Subtract Negative Numbers 4
- Multiply and Divide Negative Numbers 1
- Multiply and Divide Negative Numbers 2
- Multiply and Divide Negative Numbers 3
- Negative Numbers: Order of Operations
- Negative Numbers with Variables 1
- Negative Numbers with Variables 2
- Negative Numbers with Variables 3
- Negative Numbers with Substitution 1
- Negative Numbers with Substitution 2
- Negative Numbers with Substitution 3
- Negative Numbers Word Problems
- Decimal Place Values 1
- Decimal Place Values 2
- Expressing Decimals as a Fraction 1
- Expressing Decimals as a Fraction 2
- Expressing Decimals as a Fraction 3
- Converting Decimals Involving Money (Cents and Dollars) 1
- Converting Decimals Involving Money (Cents and Dollars) 2
- Converting Decimals Involving Money (Cents and Dollars) 3
- Add and Subtract Decimals 1
- Add and Subtract Decimals 2
- Add and Subtract Decimals 3
- Add and Subtract Decimals 4
- Multiply Decimals 1
- Multiply Decimals 2
- Multiply Decimals 3
- Divide Decimals 1
- Divide Decimals 2
- Divide Decimals 3
- Divide Decimals 4
- Converting Fractions to Decimals 1
- Converting Fractions to Decimals 2
- Converting Fractions to Decimals 3
- Rounding Whole Numbers 1
- Rounding Decimals 1
- Rounding Decimals 2
- Rounding Decimals 3
- Decimal Word Problems: Addition and Subtraction 1
- Decimal Word Problems: Addition and Subtraction 2
- Decimal Word Problems: Addition and Subtraction 3
- Decimal Word Problems: Multiplication 1
- Decimal Word Problems: Multiplication 2
- Decimal Word Problems: Multiplication 3
- Decimal Word Problems: Division 1
- Decimal Word Problems: Division 2
- One Step Equations – Add and Subtract 1
- One Step Equations – Add and Subtract 2
- One Step Equations – Add and Subtract 3
- One Step Equations – Add and Subtract 4
- One Step Equations – Multiply and Divide 1
- One Step Equations – Multiply and Divide 2
- One Step Equations – Multiply and Divide 3
- One Step Equations – Multiply and Divide 4
- Two Step Equations 1
- Two Step Equations 2
- Two Step Equations 3
- Two Step Equations 4
- Multi-Step Equations 1
- Multi-Step Equations 2
- Solve Equations using the Distributive Property 1
- Solve Equations using the Distributive Property 2
- Solve Equations using the Distributive Property 3
- Equations with Variables on Both Sides 1
- Equations with Variables on Both Sides 2
- Equations with Variables on Both Sides 3
- Equations with Variables on Both Sides (Fractions) 1
- Equations with Variables on Both Sides (Fractions) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 1
- Solve Equations – Variables on Both Sides (Distributive Property) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 3
- Solve Equations – Variables on Both Sides (Distributive Property) 4
- Writing Equations 1
- Writing Equations 2
- Writing Equations 3
- Writing Equations 4
- Equation Word Problems (Age) 1
- Equation Word Problems (Money) 1
- Equation Word Problems (Harder) 1
- Equation Problems with Substitution 1
- Equation Problems (Geometry) 1
- Equation Problems (Geometry) 2
- Equation Problems (Perimeter)
- Equation Problems (Area)
- Solve for a Variable or Formula 1
- Solve for a Variable or Formula 2
- Solve for a Variable or Formula 3
- One Step Equations – Add and Subtract 1
- One Step Equations – Add and Subtract 2
- One Step Equations – Add and Subtract 3
- One Step Equations – Add and Subtract 4
- One Step Equations – Multiply and Divide 1
- One Step Equations – Multiply and Divide 2
- One Step Equations – Multiply and Divide 3
- One Step Equations – Multiply and Divide 4
- Two Step Equations 1
- Two Step Equations 2
- Two Step Equations 3
- Two Step Equations 4
- Multi-Step Equations 1
- Multi-Step Equations 2
- Solve Equations using the Distributive Property 1
- Solve Equations using the Distributive Property 2
- Solve Equations using the Distributive Property 3
- Equations with Variables on Both Sides 1
- Equations with Variables on Both Sides 2
- Equations with Variables on Both Sides 3
- Equations with Variables on Both Sides (Fractions) 1
- Equations with Variables on Both Sides (Fractions) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 1
- Solve Equations – Variables on Both Sides (Distributive Property) 2
- Solve Equations – Variables on Both Sides (Distributive Property) 3
- Solve Equations – Variables on Both Sides (Distributive Property) 4
- Writing Equations 1
- Writing Equations 2
- Writing Equations 3
- Writing Equations 4
- Equation Word Problems (Age) 1
- Equation Word Problems (Money) 1
- Equation Word Problems (Harder) 1
- Equation Problems with Substitution 1
- Equation Problems (Geometry) 1
- Equation Problems (Geometry) 2
- Equation Problems (Perimeter)
- Equation Problems (Area)
- Solve for a Variable or Formula 1
- Solve for a Variable or Formula 2
- Solve for a Variable or Formula 3
- Factorial Notation
- Fundamental Counting Principle 1
- Fundamental Counting Principle 2
- Fundamental Counting Principle 3
- Combinations 1
- Combinations 2
- Combinations with Restrictions 1
- Combinations with Restrictions 2
- Combinations with Probability
- Basic Permutations 1
- Basic Permutations 2
- Basic Permutations 3
- Permutation Problems 1
- Permutation Problems 2
- Permutations with Repetitions 1
- Permutations with Repetitions 2
- Permutations with Restrictions 1
- Permutations with Restrictions 2
- Permutations with Restrictions 3
- Permutations with Restrictions 4
- Factorial Notation
- Fundamental Counting Principle 1
- Fundamental Counting Principle 2
- Fundamental Counting Principle 3
- Combinations 1
- Combinations 2
- Combinations with Restrictions 1
- Combinations with Restrictions 2
- Combinations with Probability
- Basic Permutations 1
- Basic Permutations 2
- Basic Permutations 3
- Permutation Problems 1
- Permutation Problems 2
- Permutations with Repetitions 1
- Permutations with Repetitions 2
- Permutations with Restrictions 1
- Permutations with Restrictions 2
- Permutations with Restrictions 3
- Permutations with Restrictions 4
- Exponent Notation 1
- Exponent Notation 2
- Exponent Notation 3
- Multiply Exponents (Product Rule) 1
- Multiply Exponents (Product Rule) 2
- Multiply Exponents (Product Rule) 3
- Multiply Exponents (Product Rule) 4
- Divide Exponents (Quotient Rule) 1
- Divide Exponents (Quotient Rule) 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Exponents 1
- Negative Exponents 2
- Negative Exponents 3
- Rational Exponents 1
- Rational Exponents 2
- Rational Exponents 3
- Mixed Operations with Exponents 1
- Mixed Operations with Exponents 2
- Exponent Notation 1
- Exponent Notation 2
- Exponent Notation 3
- Multiply Exponents (Product Rule) 1
- Multiply Exponents (Product Rule) 2
- Multiply Exponents (Product Rule) 3
- Multiply Exponents (Product Rule) 4
- Divide Exponents (Quotient Rule) 1
- Divide Exponents (Quotient Rule) 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Exponents 1
- Negative Exponents 2
- Negative Exponents 3
- Rational Exponents 1
- Rational Exponents 2
- Rational Exponents 3
- Mixed Operations with Exponents 1
- Mixed Operations with Exponents 2
- Exponent Notation 1
- Exponent Notation 2
- Exponent Notation 3
- Multiply Exponents (Product Rule) 1
- Multiply Exponents (Product Rule) 2
- Multiply Exponents (Product Rule) 3
- Multiply Exponents (Product Rule) 4
- Divide Exponents (Quotient Rule) 1
- Divide Exponents (Quotient Rule) 2
- Powers of a Power 1
- Powers of a Power 2
- Powers of a Power 3
- Powers of a Power 4
- Zero Powers 1
- Zero Powers 2
- Negative Exponents 1
- Negative Exponents 2
- Negative Exponents 3
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras Problems 1
- Pythagoras Problems 2
- Pythagoras Problems 3
- Pythagoras Mixed Review 1
- Pythagoras Mixed Review 2
- Pythagoras Mixed Review 3
- Pythagoras Mixed Review 4
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras Problems 1
- Pythagoras Problems 2
- Pythagoras Problems 3
- Pythagoras Mixed Review 1
- Pythagoras Mixed Review 2
- Pythagoras Mixed Review 3
- Pythagoras Mixed Review 4
- Complementary and Supplementary Angles 1
- Complementary and Supplementary Angles 2
- Complementary and Supplementary Angles 3
- Vertical, Revolution and Reflex Angles 1
- Vertical, Revolution and Reflex Angles 2
- Alternate, Corresponding and Co-Interior Angles 1
- Alternate, Corresponding and Co-Interior Angles 2
- Alternate, Corresponding and Co-Interior Angles 3
- Angles and Parallel Lines
- Triangle Geometry 1
- Triangle Geometry 2
- Triangle Geometry 3
- Quadrilateral Geometry 1
- Quadrilateral Geometry 2
- Ratios 1
- Ratios 2
- Ratios 3
- Ratios 4
- Proportions 1
- Proportions 2
- Dividing Quantities
- Rates 1
- Rates 2
- Rates 3
- Rates 4
- Scales 1
- Scales 2
- Scales 3
- Vertical Translations (Shifts) 1
- Vertical Translations (Shifts) 2
- Vertical Translations (Shifts) from a Point
- Horizontal Translations (Shifts) 1
- Horizontal Translations (Shifts) from a Point
- Horizontal Translations (Shifts) from a Graph
- Horizontal and Verticals Translations (Shifts) from a Graph
- Sketch a Graph using Translations (Shifts)
- Write the Equation from a Graph
- Write the Equation from Translations (Shifts) 1
- Vertical Dilations (Stretch/Shrink)
- Horizontal Dilations (Stretch/Shrink) 1
- Horizontal Dilations (Stretch/Shrink) 2
- Horizontal Dilations (Stretch/Shrink) – Scale Factor
- Horizontal and Vertical Dilations (Stretch/Shrink) 1
- Horizontal and Vertical Dilations (Stretch/Shrink) 2
- Horizontal and Vertical Dilations (Stretch/Shrink) 3
- Graphing Reflections 1
- Graphing Reflections 2
- Reflection with Rotation
- Combinations of Transformations: Order
- Combinations of Transformations: Coordinates
- Combinations of Transformations: Find Equation 1
- Combinations of Transformations: Find Equation 2
- Combinations of Transformations: Find Equation 3
- Simplify Square Roots 1
- Simplify Square Roots 2
- Simplify Square Roots 3
- Simplify Square Roots 4
- Simplify Radicals with Variables 1
- Simplify Radicals with Variables 2
- Simplify Radicals with Variables 3
- Rewriting Entire and Mixed Radicals 1
- Rewriting Entire and Mixed Radicals 2
- Add and Subtract Radical Expressions (Basic) 1
- Add and Subtract Radical Expressions (Basic) 2
- Add and Subtract Radical Expressions (Basic) 3
- Add and Subtract Radical Expressions 1
- Add and Subtract Radical Expressions 2
- Add and Subtract Radical Expressions 3
- Multiply Radical Expressions 1
- Multiply Radical Expressions 2
- Multiply Radical Expressions 3
- Multiply Radical Expressions 4
- Divide Radical Expressions 1
- Divide Radical Expressions 2
- Divide Radical Expressions 3
- Multiply and Divide Radical Expressions
- Simplify Radical Expressions using the Distributive Property 1
- Simplify Radical Expressions using the Distributive Property 2
- Simplify Radical Expressions using the Distributive Property 3
- Simplify Binomial Radical Expressions using the FOIL Method 1
- Simplify Binomial Radical Expressions using the FOIL Method 2
- Rationalizing the Denominator 1
- Rationalizing the Denominator 2
- Rationalizing the Denominator 3
- Rationalizing the Denominator 4
- Rationalizing the Denominator using Conjugates
- Simplify Square Roots 1
- Simplify Square Roots 2
- Simplify Square Roots 3
- Simplify Square Roots 4
- Simplify Radicals with Variables 1
- Simplify Radicals with Variables 2
- Simplify Radicals with Variables 3
- Rewriting Entire and Mixed Radicals 1
- Rewriting Entire and Mixed Radicals 2
- Add and Subtract Radical Expressions (Basic) 1
- Add and Subtract Radical Expressions (Basic) 2
- Add and Subtract Radical Expressions (Basic) 3
- Add and Subtract Radical Expressions 1
- Add and Subtract Radical Expressions 2
- Add and Subtract Radical Expressions 3
- Multiply Radical Expressions 1
- Multiply Radical Expressions 2
- Multiply Radical Expressions 3
- Multiply Radical Expressions 4
- Divide Radical Expressions 1
- Divide Radical Expressions 2
- Divide Radical Expressions 3
- Multiply and Divide Radical Expressions
- Simplify Radical Expressions using the Distributive Property 1
- Simplify Radical Expressions using the Distributive Property 2
- Simplify Radical Expressions using the Distributive Property 3
- Simplify Binomial Radical Expressions using the FOIL Method 1
- Simplify Binomial Radical Expressions using the FOIL Method 2
- Rationalizing the Denominator 1
- Rationalizing the Denominator 2
- Rationalizing the Denominator 3
- Rationalizing the Denominator 4
- Rationalizing the Denominator using Conjugates
- Add & Subtract Matrices 1
- Add & Subtract Matrices 2
- Add & Subtract Matrices 3
- Multiply Matrices 1
- Multiply Matrices 2
- Matrices: Multiplication Word Problems
- Determinant of a Matrix
- Inverse of a Matrix
- Matrices: Systems of Equations 1
- Matrices: Systems of Equations 2
- Gauss Jordan Elimination
- Cramer’s Rule
- Solve a System of Equations by Graphing
- Substitution Method 1
- Substitution Method 2
- Substitution Method 3
- Substitution Method 4
- Elimination Method 1
- Elimination Method 2
- Elimination Method 3
- Elimination Method 4
- Systems of Nonlinear Equations
- Systems of Equations Word Problems 1
- Systems of Equations Word Problems 2
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Solve a System of Equations by Graphing
- Substitution Method 1
- Substitution Method 2
- Substitution Method 3
- Substitution Method 4
- Elimination Method 1
- Elimination Method 2
- Elimination Method 3
- Elimination Method 4
- Systems of Nonlinear Equations
- Systems of Equations Word Problems 1
- Systems of Equations Word Problems 2
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Greatest Common Factor 1
- Greatest Common Factor 2
- Factor Expressions using GCF
- Factor Expressions 1
- Factor Expressions 2
- Factor Expressions with Negative Numbers
- Factor Difference of Two Squares 1
- Factor Difference of Two Squares 2
- Factor Difference of Two Squares 3
- Factor by Grouping
- Factor Difference of Two Squares (Harder) 1
- Factor Difference of Two Squares (Harder) 2
- Factor Difference of Two Squares (Harder) 3
- Factor Quadratics 1
- Factor Quadratics 2
- Factor Quadratics 3
- Factor Quadratics with Leading Coefficient more than 1 (1)
- Factor Quadratics with Leading Coefficient more than 1 (2)
- Factor Quadratics with Leading Coefficient more than 1 (3)
- Factor Quadratics (Complex)
- Solve Quadratics by Factoring 1
- Solve Quadratics by Factoring 2
- The Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Combining Methods for Solving Quadratic Equations
- Convert Between Logarithmic and Exponent Form 1
- Convert Between Logarithmic and Exponent Form 2
- Evaluate Logarithms 1
- Evaluate Logarithms 2
- Evaluate Logarithms 3
- Expand Log Expressions
- Simplify Log Expressions 1
- Simplify Log Expressions 2
- Simplify Log Expressions 3
- Logarithmic Equations 1
- Logarithmic Equations 2
- Logarithmic Equations 3
- Change Of Base Formula
- Solving Exponential Equations Using Log Laws
- Simplify Roots of Negative Numbers 1
- Simplify Roots of Negative Numbers 2
- Powers of the Imaginary Unit 1
- Powers of the Imaginary Unit 2
- Solve Quadratic Equations with Complex Solutions 1
- Solve Quadratic Equations with Complex Solutions 2
- Equality of Complex Numbers
- Add and Subtract Complex Numbers 1
- Add and Subtract Complex Numbers 2
- Multiply Complex Numbers 1
- Multiply Complex Numbers 2
- Divide Complex Numbers
- Complex Numbers – Product of Linear Factors 1
- Complex Numbers – Product of Linear Factors 2
- Mixed Operations with Complex Numbers
- One Step Inequalities 1
- One Step Inequalities 2
- Two Step Inequalities
- Multi-Step Inequalities 1
- Multi-Step Inequalities 2
- Compound Inequalities 1
- Compound Inequalities 2
- Compound Inequalities 3
- Inequality Word Problems 1
- Inequality Word Problems 2
- One Step Inequalities 1
- One Step Inequalities 2
- Two Step Inequalities
- Multi-Step Inequalities 1
- Multi-Step Inequalities 2
- Compound Inequalities 1
- Compound Inequalities 2
- Compound Inequalities 3
- Inequality Word Problems 1
- Inequality Word Problems 2
- Absolute Value Inequalities
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Simplify Algebraic Expressions 1
- Simplify Algebraic Expressions 2
- Simplify Algebraic Expressions 3
- Substitution and Evaluating Algebraic Expressions
- Substitution and Evaluating Multi-Variable Algebraic Expressions
- Substitution and Evaluating Rational Algebraic Expressions
- Substitution and Evaluating Algebraic Expressions with Negative Numbers 1
- Substitution and Evaluating Algebraic Expressions with Negative Numbers 2
- Simplify Algebraic Expressions using the Distributive Property 1
- Simplify Algebraic Expressions using the Distributive Property 2
- Simplify Algebraic Expressions using the Distributive Property 3
- Write Algebraic Expressions from Diagrams
- Evaluate Algebraic Expressions Problems
- Combine Like Terms 1
- Combine Like Terms 2
- Combine Like Terms 3
- Simplify Algebraic Expressions 1
- Simplify Algebraic Expressions 2
- Simplify Algebraic Expressions 3
- Substitution and Evaluating Algebraic Expressions
- Substitution and Evaluating Multi-Variable Algebraic Expressions
- Substitution and Evaluating Rational Algebraic Expressions
- Substitution and Evaluating Algebraic Expressions with Negative Numbers 1
- Substitution and Evaluating Algebraic Expressions with Negative Numbers 2
- Simplify Algebraic Expressions using the Distributive Property 1
- Simplify Algebraic Expressions using the Distributive Property 2
- Simplify Algebraic Expressions using the Distributive Property 3
- Write Algebraic Expressions from Diagrams
- Evaluate Algebraic Expressions Problems
- Combine Like Terms 1
- Combine Like Terms 2
- Combine Like Terms 3
- Compass Bearings and True Bearings 1
- Compass Bearings and True Bearings 2
- Solving for Bearings
- Bearings from Opposite Direction
- Using Bearings to Find Distance 1
- Using Bearings to Find Distance 2
- Using Bearings to Find Distance 3
- Using Bearings and Distances to Find Angles
- Working with Radial Surveys 1
- Working with Radial Surveys 2
- Working with Radial Surveys 3
- Working with Radial Surveys 4
- Multiply Binomials
- Multiply Binomials – FOIL Method
- FOIL Method – Same First Variable 1
- FOIL Method – Same First Variable 2
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Difference of Two Squares (Longer Expressions)
- Greatest Common Factor 1
- Greatest Common Factor 2
- Factor Expressions using GCF
- Factor Expressions 1
- Factor Expressions 2
- Factor Expressions with Negative Numbers
- Factor Difference of Two Squares 1
- Factor Difference of Two Squares 2
- Factor Difference of Two Squares 3
- Factor by Grouping
- Factor Difference of Two Squares (Harder) 1
- Factor Difference of Two Squares (Harder) 2
- Factor Difference of Two Squares (Harder) 3
- Factor Quadratics 1
- Factor Quadratics 2
- Factor Quadratics 3
- Factor Quadratics with Leading Coefficient more than 1 (1)
- Factor Quadratics with Leading Coefficient more than 1 (2)
- Factor Quadratics with Leading Coefficient more than 1 (3)
- Factor Quadratics (Complex)
- Convert Measurements (Length) 1
- Convert Measurements (Length) 2
- Convert Measurements (Volume) 1
- Convert Measurements (Volume) 2
- Convert Measurements (Mass) 1
- Convert Measurements (Mass) 2
- Add & Subtract Matrices 1
- Add & Subtract Matrices 2
- Add & Subtract Matrices 3
- Multiply Matrices 1
- Multiply Matrices 2
- Matrices: Multiplication Word Problems
- Determinant of a Matrix
- Inverse of a Matrix
- Matrices: Systems of Equations 1
- Matrices: Systems of Equations 2
- Gauss Jordan Elimination
- Cramer’s Rule
- Add and Subtract Negative Numbers on the Number Line 1
- Add and Subtract Negative Numbers on the Number Line 2
- Add and Subtract Negative Numbers on the Number Line 3
- Add and Subtract Negative Numbers on the Number Line 4
- Add and Subtract Negative Numbers 1
- Add and Subtract Negative Numbers 2
- Add and Subtract Negative Numbers 3
- Add and Subtract Negative Numbers 4
- Multiply and Divide Negative Numbers 1
- Multiply and Divide Negative Numbers 2
- Multiply and Divide Negative Numbers 3
- Negative Numbers: Order of Operations
- Negative Numbers with Variables 1
- Negative Numbers with Variables 2
- Negative Numbers with Variables 3
- Negative Numbers with Substitution 1
- Negative Numbers with Substitution 2
- Negative Numbers with Substitution 3
- Negative Numbers Word Problems
- Convert To and From Scientific Notation
- Multiply & Divide in Scientific Notation
- Scientific Notation Word Problems
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras Problems 1
- Pythagoras Problems 2
- Pythagoras Problems 3
- Pythagoras Mixed Review 1
- Pythagoras Mixed Review 2
- Pythagoras Mixed Review 3
- Pythagoras Mixed Review 4
- Increase and Decrease an Amount by a Percent – Word Problems 1
- Increase and Decrease an Amount by a Percent – Word Problems 2
- Percent of Change
- Percent of Change – Word Problems
- Percent of an Amount – Word Problems 1
- Percent of an Amount – Word Problems 2
- Ratios 1
- Ratios 2
- Ratios 3
- Ratios 4
- Proportions 1
- Proportions 2
- Dividing Quantities
- Rates 1
- Rates 2
- Rates 3
- Rates 4
- Scales 1
- Scales 2
- Scales 3
- Increase and Decrease an Amount by a Percent – Word Problems 1
- Increase and Decrease an Amount by a Percent – Word Problems 2
- Percent of Change
- Percent of Change – Word Problems
- Percent of an Amount – Word Problems 1
- Percent of an Amount – Word Problems 2
- Find Mean, Mode, Median and Range 1
- Find Mean, Mode, Median and Range 2
- Find Mean, Mode, Median and Range 3
- Create Frequency Tables & Graphs
- Interpret Frequency Tables 1
- Interpret Frequency Tables 2
- Create and Interpret Bar & Line Graphs (Histograms)
- Interpret Cumulative Frequency Tables and Charts 1
- Interpret Cumulative Frequency Tables and Charts 2
- Create Grouped Frequency Tables and Graphs
- Interpret Grouped Frequency Tables
- Create and Interpret Dot Plots (Line Plots) 1
- Create and Interpret Dot Plots (Line Plots) 2
- Finding the Interquartile Range 1
- Finding the Interquartile Range 2
- Create and Interpret Box & Whisker Plots 1
- Create and Interpret Box & Whisker Plots 2
- Create and Interpret Box & Whisker Plots 3
- Create and Interpret Box & Whisker Plots 4
- Create and Interpret Stem & Leaf Plots 1
- Create and Interpret Stem & Leaf Plots 2
- Create and Interpret Stem & Leaf Plots 3
- Create and Interpret Stem & Leaf Plots 4
- Mean and Standard Deviation
- The Normal Curve 1
- The Normal Curve 2
- The Normal Curve 3
- Z-Values (Z-Scores)
- Vertices and Edges
- Degrees 1
- Degrees 2
- Degrees 3
- Drawing a Network 1
- Drawing a Network 2
- Completing a Table from a Network Diagram
- Network from Maps and Plans
- Identify Paths and Cycles
- Eulerian Trails and Circuits 1
- Eulerian Trails and Circuits 2
- Identify Spanning Trees
- Minimum Spanning Trees 1
- Minimum Spanning Trees 2
- Shortest Path 1
- Shortest Path 2
- Convert Units of Time 1
- Convert Units of Time 2
- Convert Units of Time 3
- Add Units of Time
- Subtract Units of Time
- Convert 12 Hour Time to 24 Hour Time 1
- Convert 12 Hour Time to 24 Hour Time 2
- Convert 12 Hour Time to 24 Hour Time 3
- Convert 24 Hour Time to 12 Hour Time 1
- Convert 24 Hour Time to 12 Hour Time 2
- Add and Subtract Time Using the Calculator
- Time Difference and Longitudes 1
- Time Difference and Longitudes 2
- Time Difference and Longitudes 3
- International Time Zones 1
- International Time Zones 2
- Time and Travelling Word Problems 1
- Time and Travelling Word Problems 2
- Great Circle Distances
- FOIL Method – 3 Terms
- Division of Polynomials
- Remainder Theorem
- Factor Theorem
- Graphing Polynomials
- Graph Polynomials
- Solve a System of Equations by Graphing
- Substitution Method
- Elimination Method
- Systems of Nonlinear Equations
- Systems of Equations Word Problems
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Convert Radians and Degrees 1
- Convert Radians and Degrees 2
- Convert Radians and Degrees 3
- Radians and Arc Length (Radians)
- Areas of Sectors and Segments (Radians)
- The Unit Circle
- Unit Circle: Find Angles
- Unit Circle: Trig Ratios
- Unit Circle: Exact Values 1
- Unit Circle: Exact Values 2
- Unit Circle: Find Angles from Equations
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)
- Intro to Trigonometric Ratios (SOH CAH TOA) 1
- Intro to Trigonometric Ratios (SOH CAH TOA) 2
- Round Angles (Degrees, Minutes, Seconds)
- Evaluate Trig Expressions using a Calculator 1
- Evaluate Trig Expressions using a Calculator 2
- Trig Ratios: Solving for a Side 1
- Trig Ratios: Solving for a Side 2
- Trig Ratios: Solving for an Angle
- Angles of Elevation and Depression
- Trig Ratios Word Problems: Solving for a Side
- Trig Ratios Word Problems: Solving for an Angle
- Area of Non-Right Angled Triangles 1
- Area of Non-Right Angled Triangles 2
- Law of Sines: Solving for a Side
- Law of Sines: Solving for an Angle
- Law of Cosines: Solving for a Side
- Law of Cosines: Solving for an Angle
- Trigonometry Word Problems 1
- Trigonometry Word Problems 2
- Trigonometry Mixed Review: Part 1 (1)
- Trigonometry Mixed Review: Part 1 (2)
- Trigonometry Mixed Review: Part 1 (3)
- Trigonometry Mixed Review: Part 1 (4)
- Trigonometry Mixed Review: Part 2 (1)
- Trigonometry Mixed Review: Part 2 (2)
- Trigonometry Mixed Review: Part 2 (3)
- Convert Radians and Degrees 1
- Convert Radians and Degrees 2
- Convert Radians and Degrees 3
- Radians and Arc Length (Radians)
- Areas of Sectors and Segments (Radians)
- The Unit Circle
- Unit Circle: Find Angles
- Unit Circle: Trig Ratios
- Unit Circle: Exact Values 1
- Unit Circle: Exact Values 2
- Unit Circle: Find Angles from Equations
- Find Base from Percent of an Amount (Unitary Method) 1
- Find Base from Percent of an Amount (Unitary Method) 2
- Using Percentages with Proportions
- Find Original Amount Before Percent Change (Unitary Method)
- Find Base from Percent of an Amount (Unitary Method) 1
- Find Base from Percent of an Amount (Unitary Method) 2
- Using Percentages with Proportions
- Find Original Amount Before Percent Change (Unitary Method)
- Derivative of Trigonometric Functions 1
- Derivative of Trigonometric Functions 2
- Derivative of Trigonometric Functions 3
- Trig Applications of Differentiation
- Integral of Trigonometric Functions 1
- Integral of Trigonometric Functions 2
- Trig Applications of Integration
- Graph Trigonometric Functions 1
- Graph Trigonometric Functions 2
- Graph Trigonometric Functions 3
- Graph Trigonometric Functions 4
- Derivative of Trigonometric Functions 1
- Derivative of Trigonometric Functions 2
- Derivative of Trigonometric Functions 3
- Trig Applications of Differentiation
- Integral of Trigonometric Functions 1
- Integral of Trigonometric Functions 1
- Trig Applications of Integration
- Graph Trigonometric Functions 1
- Graph Trigonometric Functions 2
- Graph Trigonometric Functions 3
- Graph Trigonometric Functions 4
- Power Rule 1
- Power Rule 2
- Power Rule 3
- Power Rule 4
- Chain Rule 1
- Chain Rule 2
- Product Rule
- Quotient Rule
- Derivatives of Exponential Functions 1
- Derivatives of Exponential Functions 2
- Derivatives of Exponential Functions 3
- Derivatives of Trigonometric Functions 1
- Derivatives of Trigonometric Functions 2
- Derivatives of Trigonometric Functions 3
- Power Rule 1
- Power Rule 2
- Power Rule 3
- Power Rule 4
- Chain Rule 1
- Chain Rule 2
- Product Rule
- Quotient Rule
- Derivatives of Exponential Functions 1
- Derivatives of Exponential Functions 2
- Derivatives of Exponential Functions 3
- Derivatives of Trigonometric Functions 1
- Derivatives of Trigonometric Functions 2
- Derivatives of Trigonometric Functions 3
- Derivatives of Exponential Functions 1
- Derivatives of Exponential Functions 2
- Derivatives of Exponential Functions 3
- Integrals of Exponential Functions
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions
- Indefinite Integrals of Logarithmic Functions 1
- Indefinite Integrals of Logarithmic Functions 2
- Direct Variation
- Inverse Variation 1
- Inverse Variation 2
- Indefinite Integrals 1
- Indefinite Integrals 2
- Indefinite Integrals 3
- Indefinite Integrals of Exponential Functions
- Indefinite Integrals of Logarithmic Functions 1
- Indefinite Integrals of Logarithmic Functions 2
- Indefinite Integrals of Trig Functions
- Definite Integrals
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions
- Definite Integrals of Trig Functions
- Areas Between Curves and the Axis 1
- Areas Between Curves and the Axis 2
- Area Between Curves
- Volumes of Revolution 1
- Volumes of Revolution 2
- Volumes of Revolution 3
- Trapezoidal Rule
- Simpsons Rule
- Applications of Integration for Trig Functions
- One Step Inequalities 1
- One Step Inequalities 2
- Two Step Inequalities
- Multi-Step Inequalities 1
- Multi-Step Inequalities 2
- Compound Inequalities 1
- Compound Inequalities 2
- Compound Inequalities 3
- Inequality Word Problems 1
- Inequality Word Problems 2
- Absolute Value Inequalities
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Multiply Binomials
- Multiply Binomials – FOIL Method
- FOIL Method – Same First Variable 1
- FOIL Method – Same First Variable 2
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Difference of Two Squares (Longer Expressions)
- Multiply Binomials
- Multiply Binomials – FOIL Method
- FOIL Method – Same First Variable 1
- FOIL Method – Same First Variable 2
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Difference of Two Squares (Longer Expressions)
- Multiply Binomials
- Multiply Binomials – FOIL Method
- FOIL Method – Same First Variable 1
- FOIL Method – Same First Variable 2
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Difference of Two Squares (Longer Expressions)
- Solving Exponential Equations
- Factorial Notation
- Fundamental Counting Principle 1
- Fundamental Counting Principle 2
- Fundamental Counting Principle 3
- Combinations 1
- Combinations 2
- Combinations with Restrictions 1
- Combinations with Restrictions 2
- Combinations with Probability
- Basic Permutations 1
- Basic Permutations 2
- Basic Permutations 3
- Permutation Problems 1
- Permutation Problems 2
- Permutations with Repetitions 1
- Permutations with Repetitions 2
- Permutations with Restrictions 1
- Permutations with Restrictions 2
- Permutations with Restrictions 3
- Permutations with Restrictions 4
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Slope of a Line 1
- Slope of a Line 2
- Slope Intercept Form: Graph an Equation 1
- Slope Intercept Form: Graph an Equation 2
- Slope Intercept Form: Write an Equation 1
- Graph Linear Inequalities 1
- Convert Standard Form and Slope Intercept Form 1
- Convert Standard Form and Slope Intercept Form 2
- Point Slope Form 1
- Point Slope Form 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2
- Simplify Roots of Negative Numbers 1
- Simplify Roots of Negative Numbers 2
- Powers of the Imaginary Unit 1
- Powers of the Imaginary Unit 2
- Solve Quadratic Equations with Complex Solutions 1
- Solve Quadratic Equations with Complex Solutions 2
- Equality of Complex Numbers
- Add and Subtract Complex Numbers 1
- Add and Subtract Complex Numbers 2
- Multiply Complex Numbers 1
- Multiply Complex Numbers 2
- Divide Complex Numbers
- Complex Numbers – Product of Linear Factors 1
- Complex Numbers – Product of Linear Factors 2
- Mixed Operations with Complex Numbers
- Solve a System of Equations by Graphing
- Substitution Method 1
- Substitution Method 2
- Substitution Method 3
- Substitution Method 4
- Elimination Method 1
- Elimination Method 2
- Elimination Method 3
- Elimination Method 4
- Systems of Nonlinear Equations
- Systems of Equations Word Problems 1
- Systems of Equations Word Problems 2
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method
- Identify Functions
- Function Notation
- Domain and Range 1
- Domain and Range 2
- Domain and Range 3
- Odd and Even Functions 1
- Odd and Even Functions 2
- Piecewise Functions
- Graphing the Intersection of Regions 1
- Graphing the Intersection of Regions 2
- Tangents and Normals
- Log and Exponential Tangents and Normals
- Increasing and Decreasing Intervals
- Relative and Absolute Maxima and Minima
- Stationary and Inflection Points
- Curve Sketching 1
- Curve Sketching 2
- Optimisation Problems
- Trig Applications of Differentiation
- Write an Equation for Circle Graphs
- Graph Circles in Standard Form
- Graph Circles in Expanded Form
- Graph Parabolas (Focus and Directrix) 1
- Graph Parabolas (Focus and Directrix) 2
- Graph Parabolas Given the Vertex, Focus and Directrix 1
- Graph Parabolas Given the Vertex, Focus and Directrix 2
- Graph Hyperbolas
- Write an Equation for Hyperbolas
- Graph Cubic Curves
- Write an Equation for Cubic Curves
- The Exponential Curve
- Write an Equation for Circle Graphs
- Graph Circles in Standard Form
- Graph Circles in Expanded Form
- Graph Parabolas (Focus and Directrix) 1
- Graph Parabolas (Focus and Directrix) 2
- Graph Parabolas Given the Vertex, Focus and Directrix 1
- Graph Parabolas Given the Vertex, Focus and Directrix 2
- Graph Hyperbolas
- Write an Equation for Hyperbolas
- Graph Cubic Curves
- Write an Equation for Cubic Curves
- The Exponential Curve
- Lowest Common Denominator
- Add & Subtract Rational Expressions
- Add & Subtract Rational Expressions with Unlike Denominators 1
- Add & Subtract Rational Expressions with Unlike Denominators 2
- Multiply & Divide Rational Expressions
- Lowest Common Denominator
- Add & Subtract Rational Expressions
- Add & Subtract Rational Expressions with Unlike Denominators 1
- Add & Subtract Rational Expressions with Unlike Denominators 2
- Multiply & Divide Rational Expressions
- Area of Shapes 1
- Area of Shapes 2
- Area of Shapes 3
- Area of Shapes 4
- Areas of Circles 1
- Areas of Circles 2
- Areas of a Shaded Region
- Area of Composite Shapes
- Area of Sectors
- Area of Shapes Mixed Review 1
- Area of Shapes Mixed Review 2
- Area of Shapes Mixed Review 3
- Area of Shapes 1
- Area of Shapes 2
- Area of Shapes 3
- Area of Shapes 4
- Areas of Circles 1
- Areas of Circles 2
- Areas of a Shaded Region
- Area of Composite Shapes
- Area of Sectors
- Area of Shapes Mixed Review 1
- Area of Shapes Mixed Review 2
- Area of Shapes Mixed Review 3
- Volume of Shapes 1
- Volume of Shapes 2
- Volume of Shapes 3
- Volume of Shapes 4
- Volume of Composite Shapes 1
- Volume of Composite Shapes 2
- Surface Area of Shapes 1
- Surface Area of Shapes 2
- Surface Area of Shapes 3
- Surface Area and Volume Mixed Review 1
- Surface Area and Volume Mixed Review 2
- Surface Area and Volume Mixed Review 3
- Surface Area and Volume Mixed Review 4
- Greatest Common Factor 1
- Greatest Common Factor 2
- Factor Expressions using GCF
- Factor Expressions 1
- Factor Expressions 2
- Factor Expressions with Negative Numbers
- Factor Difference of Two Squares 1
- Factor Difference of Two Squares 2
- Factor Difference of Two Squares 3
- Factor by Grouping
- Factor Difference of Two Squares (Harder) 1
- Factor Difference of Two Squares (Harder) 2
- Factor Difference of Two Squares (Harder) 3
- Factor Quadratics 1
- Factor Quadratics 2
- Factor Quadratics 3
- Factor Quadratics with Leading Coefficient more than 1 (1)
- Factor Quadratics with Leading Coefficient more than 1 (2)
- Factor Quadratics with Leading Coefficient more than 1 (3)
- Factor Quadratics (Complex)
- Simple Probability 1
- Simple Probability 2
- Simple Probability 3
- Simple Probability 4
- Complementary Probability 1
- Compound Events 1
- Compound Events 2
- Venn Diagrams (Non Mutually Exclusive)
- Independent Events 1
- Independent Events 2
- Dependent Events (Conditional Probability)
- Probability Tree (Independent) 1
- Probability Tree (Independent) 2
- Probability Tree (Dependent)
- Simple Probability 1
- Simple Probability 2
- Simple Probability 3
- Simple Probability 4
- Complementary Probability 1
- Compound Events 1
- Compound Events 2
- Venn Diagrams (Non Mutually Exclusive)
- Independent Events 1
- Independent Events 2
- Dependent Events (Conditional Probability)
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras’ Theorem Problems 1
- Pythagoras’ Theorem Problems 2
- Pythagoras’ Theorem Problems 3
- Pythagoras Theorem Mixed Review 1
- Pythagoras Theorem Mixed Review 2
- Pythagoras Theorem Mixed Review 3
- Pythagoras Theorem Mixed Review 4
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint Formula 1
- Midpoint Formula 2
- Midpoint Formula 3
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2
- Solve Quadratics by Factoring 1
- Solve Quadratics by Factoring 2
- The Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Congruent Triangles 1
- Congruent Triangles 2
- Pythagoras’ Theorem Problems 1
- Pythagoras’ Theorem Problems 2
- Pythagoras’ Theorem Problems 3
- Solve Quadratics by Factoring
- The Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Combining Methods for Solving Quadratic Equations
- Solve Quadratics by Factoring
- The Quadratic Formula
- Completing the Square 1
- Completing the Square 2
- Intro to Quadratic Functions (Parabolas) 1
- Intro to Quadratic Functions (Parabolas) 2
- Intro to Quadratic Functions (Parabolas) 3
- Graph Quadratic Functions in Standard Form 1
- Graph Quadratic Functions in Standard Form 2
- Graph Quadratic Functions by Completing the Square
- Graph Quadratic Functions in Vertex Form
- Write a Quadratic Equation from the Graph
- Write a Quadratic Equation Given the Vertex and Another Point
- Quadratic Inequalities 1
- Quadratic Inequalities 2
- Quadratics Word Problems 1
- Quadratics Word Problems 2
- Quadratic Identities
- Graphing Quadratics Using the Discriminant
- Positive and Negative Definite
- Applications of the Discriminant 1
- Applications of the Discriminant 2
- Combining Methods for Solving Quadratic Equations
- Power Rule 1
- Power Rule 2
- Power Rule 3
- Power Rule 4
- Chain Rule 1
- Chain Rule 2
- Product Rule
- Quotient Rule
- Derivatives of Exponential Functions 1
- Derivatives of Exponential Functions 2
- Derivatives of Exponential Functions 3
- Derivatives of Trigonometric Functions 1
- Derivatives of Trigonometric Functions 2
- Derivatives of Trigonometric Functions 3
- Power Rule 1
- Power Rule 2
- Power Rule 3
- Power Rule 4
- Chain Rule 1
- Chain Rule 2
- Product Rule
- Quotient Rule
- Derivatives of Exponential Functions 1
- Derivatives of Exponential Functions 2
- Derivatives of Exponential Functions 3
- Derivatives of Trigonometric Functions 1
- Derivatives of Trigonometric Functions 2
- Derivatives of Trigonometric Functions 3
- Tangents and Normals
- Log and Exponential Tangents and Normals
- Increasing and Decreasing Intervals
- Critical Points (Maximum and Minimum Values)
- Stationary and Inflection Points
- Curve Sketching 1
- Curve Sketching 2
- Optimization
- Tangents and Normals
- Log and Exponential Tangents and Normals
- Increasing and Decreasing Intervals
- Critical Points (Maximum and Minimum Values)
- Stationary and Inflection Points
- Curve Sketching 1
- Curve Sketching 2
- Optimization
- Antiderivatives (Indefinite Integrals) 1
- Antiderivatives (Indefinite Integrals) 2
- Antiderivatives (Indefinite Integrals) 3
- Antiderivatives of Exponential Functions
- Antiderivatives of Logarithmic Functions 1
- Antiderivatives of Logarithmic Functions 2
- Antiderivatives of Trig Functions 1
- Antiderivatives of Trig Functions 2
- Definite Integrals
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions
- Antiderivatives (Indefinite Integrals) 1
- Antiderivatives (Indefinite Integrals) 2
- Antiderivatives (Indefinite Integrals) 3
- Antiderivatives of Exponential Functions
- Antiderivatives of Logarithmic Functions 1
- Antiderivatives of Logarithmic Functions 2
- Antiderivatives of Trig Functions 1
- Antiderivatives of Trig Functions 2
- Definite Integrals
- Definite Integrals of Exponential Functions
- Definite Integrals of Logarithmic Functions
- Areas Between Curves and the Axis 1
- Areas Between Curves and the Axis 2
- Area Between Two Curves
- Volumes of Solids 1
- Volumes of Solids 2
- Volumes of Solids 3
- Areas Between Curves and the Axis 1
- Areas Between Curves and the Axis 2
- Area Between Two Curves
- Volumes of Solids 1
- Volumes of Solids 2
- Volumes of Solids 3
- Intro to Sequences
- Arithmetic Series (Sum)
- Geometric Series (Sum)
- Infinite Geometric Series