Substitution Method 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- Answered
- Review
-
Question 1 of 5
1. Question
Solve the following systems of equations by substitution.`x-y=8``2x+y=1`-
`x=` (3)`y=` (-5)
Hint
Help VideoCorrect
Great Work!
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.`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` -
-
Question 2 of 5
2. Question
Solve the following systems of equations by substitution.`2a+b=5``5a-3b=7`-
`a=` (2)`b=` (1)
Hint
Help VideoCorrect
Keep Going!
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.`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` -
-
Question 3 of 5
3. Question
Solve the following systems of equations by substitution.`x-y=1``2x+y=11`-
`x=` (4)`y=` (3)
Hint
Help VideoCorrect
Great Work!
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.`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` -
-
Question 4 of 5
4. Question
Solve the following systems of equations by substitution.`a-3b=2``2a-b=14`-
`a=` (8)`b=` (2)
Hint
Help VideoCorrect
Keep Going!
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-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` -
-
Question 5 of 5
5. Question
Solve the following systems of equations by substitution.`2x+5y=7``x-y=7`-
`x=` (6)`y=` (-1)
Hint
Help VideoCorrect
Excellent!
Incorrect
Substitution 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` -
Quizzes
- 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