Substitution Method 4
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Question 1 of 4
1. Question
Solve the following systems of equations by substitution.`b=2a+2``2a+5b=10`-
`a=` (0)`b=` (2)
Hint
Help VideoCorrect
Well Done!
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.`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 2 of 4
2. Question
Solve the following systems of equations by substitution.`2m+5n=5``m-5n=10`-
`m=` (5)`n=` (-1)
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.`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 3 of 4
3. Question
Solve the following systems of equations by substitution.`4x-5y=14``2x+3y=-4`-
`x=` (1)`y=` (-2)
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.`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 4 of 4
4. Question
Solve the following systems of equations by substitution.`7x-2y=6``3x+4y=22`-
`x=` (2)`y=` (4)
Hint
Help VideoCorrect
Well Done!
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.`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
- 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