Substitution Method 2
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Question 1 of 5
1. Question
Solve the following systems of equations by substitution.`2x-y=6``x+3y=10`-
`x=` (4)`y=` (2)
Hint
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Correct!
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The substitution method removes one of the variables by replacement in a pair of systems of 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 2 of 5
2. Question
Solve the following systems of equations by substitution.`2x+y=1``x-y=2`-
`x=` (1)`y=` (-1)
Hint
Help VideoCorrect
Fantastic!
Incorrect
The substitution method removes one of the variables by replacement in a pair of systems of 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 3 of 5
3. Question
Solve the following systems of equations by substitution.`2x+y=7``4x-2y=10`-
`x=` (3)`y=` (1)
Hint
Help VideoCorrect
Correct!
Incorrect
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+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 4 of 5
4. Question
Solve the following systems of equations by substitution.`3x-2y=20``x+2y=-4`-
`x=` (4)`y=` (-4)
Hint
Help VideoCorrect
Fantastic!
Incorrect
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.`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 5 of 5
5. Question
Solve the following systems of equations by substitution.`a-b=5``2a+b=4`-
`a=` (3)`b=` (-2)
Hint
Help VideoCorrect
Nice Job!
Incorrect
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.`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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