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3 Variable Systems of Equations - Substitution Method>
3 Variable Systems of Equations – Substitution Method3 Variable Systems of Equations – Substitution Method
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Question 1 of 2
1. Question
Solve the following systems of equations by substitution.`a-2b+c=-4``2a+2b-c=10``-3a-b-4c=9`-
`a=` (2)`b=` (1)`c=` (-4)
Hint
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Fantastic!
Incorrect
Substitution Method
- `1)` Make one variable the subject in one equation
- `2)` Substitute this variable in to the other two equations
- `3)` Solve these two equations using substitution and find `2` variables
- `4)` Substitute the `2` variables into the original equation
First, label the equations `1`, `2` and `3` respectively.`a-2b+c` `=` `-4` Equation `1` `2a+2b-c` `=` `10` Equation `2` `-3a-b-4c` `=` `9` Equation `3` Next, make `a` the subject in Equation `1`.`a-2b+c` `=` `-4` `a-2b+c` `+(2b-c)` `=` `-4` `+(2b-c)` Add `2b-c` to both sides `a` `=` `2b-c-4` Simplify Substitute Equation `1`’s `a` into both Equations `2` and `3`. Label the results as Equations `A` and `B``2``a``+2b-c` `=` `10` Equation `2` `2(``2b-c-4``)+2b-c` `=` `10` `a=2b-c-4` `4b-2c-8+2b-c` `=` `10` Distribute `2` inside the parenthesis `6b-3c-8` `=` `10` Simplify `6b-3c-8` `+8` `=` `10` `+8` Add `8` to both sides `6b-3c` `=` `18` Equation `A` `-3``a``-b-4c` `=` `9` Equation `3` `-3(``2b-c-4``)-b-4c` `=` `9` `a=2b-c-4` `-6b+3c+12-b-4c` `=` `9` Distribute `2` inside the parenthesis `-7b-c+12` `=` `9` Simplify `-7b-c+12` `-12` `=` `9` `-12` Subtract `12` from both sides `-7b-c` `=` `-3` Equation `B` Next, make `c` the subject in Equation `B`.`-7b-c` `=` `-3` Equation `B` `-7b-c` `+c` `=` `-3` `+c` Add `c` to both sides `-7b` `=` `-3+c` `-7b` `+3` `=` `-3+c` `+3` Add `3` to both sides `-7b+3` `=` `c` `c` `=` `-7b+3` Now, substitute `c=-7b+3` into Equation `A` and solve for `b`.`6b-3``c` `=` `18` Equation `A` `6b-3(``-7b+3``)` `=` `18` `c=-7b+3` `6b+21b-9` `=` `18` Distribute `3` inside the parenthesis `27b-9` `=` `18` Simplify `27b-9` `+9` `=` `18` `+9` Add `9` to both sides `27b` `=` `27` `27b` `div27` `=` `27` `div27` Divide both sides by `27` `b` `=` `1` Next, substitute the value of `b` into Equation `B` and solve for `c``c` `=` `-7``b` `+3` Equation `B` `c` `=` `-7(``1``)+3` `b=1` `c` `=` `-7+3` `c` `=` `-4` Finally, substitute the known values of `b` and `c` into Equation `1` to solve for `a`.`a-2``b``+``c` `=` `-4` Equation `1` `a-2(``1``)+``-4` `=` `-4` `b=1` and `c=-4` `a-2-4` `=` `-4` `a-6` `=` `-4` Simplify `a-6` `+6` `=` `-4` `+6` Add `6` to both sides `a` `=` `2` `a=2``b =1``c =-4` -
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Question 2 of 2
2. Question
Solve the following systems of equations by substitution.`3x-3y+z=-2``2y-z=-5``x+4y+2z=-9`-
`x=` (-3)`y=` (-2)`z=` (1)
Hint
Help VideoCorrect
Correct!
Incorrect
Substitution Method
- `1)` Make one variable the subject in one equation
- `2)` Substitute this variable in to the other two equations
- `3)` Solve these two equations using substitution and find `2` variables
- `4)` Substitute the `2` variables into the original equation
First, label the equations `1`, `2` and `3` respectively.`3x-3y+z` `=` `-2` Equation `1` `2y-z` `=` `-5` Equation `2` `x+4y+2z` `=` `-9` Equation `3` Next, make `z` the subject in Equation `1`.`2y-z` `=` `-5` `2y-z` `+5` `=` `-5` `+5` Add `5` to both sides `2y-z+5` `=` `0` `2y+5-z` `+z` `=` `0` `+z` Add `z` to both sides `2y+5` `=` `z` `z` `=` `2y+5` Simplify Substitute `z=2y+5` into both Equations `1` and `3`. Label the results as Equations `A` and `B``3x-3y+``z` `=` `-2` Equation `1` `3x-3y+``2y+5` `=` `-2` `z=2y+5` `3x-y+5` `=` `-2` Combine like terms `3x-y+5` `-5` `=` `-2` `-5` Subtract `5` from both sides `3x-y` `=` `-7` Equation `A` `x+4y+2``z` `=` `-9` Equation `3` `x+4y+2(``2y+5``)` `=` `-9` `z=2y+5` `x+4y+4y+10` `=` `-9` Distribute `2` inside the parenthesis `x+8y+10` `=` `-9` Combine like terms `x+8y+10` `-10` `=` `-9` `-10` Subtract `10` from both sides `x+8y` `=` `-19` Equation `B` Next, make `y` the subject in Equation `A`.`3x-y` `=` `-7` Equation `A` `3x-y` `+7` `=` `-7` `+7` Add `7` to both sides `3x+7-y` `=` `0` `3x+7-y` `+y` `=` `0` `+y` Add `y` to both sides `3x+7` `=` `y` `y` `=` `3x+7` Now, substitute `y=3x+7` into Equation `B` and solve for `x`.`x+8``y` `=` `-19` Equation `B` `x+8(``3x+7``)` `=` `-19` `y=3x+7` `x+24x+56` `=` `-19` Distribute `8` inside the parenthesis `25x+56` `=` `-19` Combine like terms `25x+56` `-56` `=` `-19` `-56` Subtract `56` from both sides `25x` `=` `-75` `27x` `div25` `=` `-75` `div25` Divide both sides by `25` `x` `=` `-3` Next, substitute the value of `x` into Equation `A` and solve for `y``3``x``-y` `=` `-7` Equation `A` `3(``-3``)-y` `=` `-7` `x=-3` `-9-y` `=` `-7` `-9-y` `+9` `=` `-7` `+9` Add `9` to both sides `-y` `=` `2` `-y` `times(-1)` `=` `2` `times(-1)` Multiply both sides by `-1` `y` `=` `-2` Finally, substitute the known value of `y` into Equation `2` to solve for `z`.`2``y``-z` `=` `-5` Equation `2` `2(``-2``)-z` `=` `-5` `y=-2` `-4-z` `=` `-5` `-4-z` `+4` `=` `-5` `+4` Add `4` to both sides `-z` `=` `-1` `-z` `times(-1)` `=` `-1` `times(-1)` Multiply both sides by `-1` `z` `=` `1` `x=-3``y =-2``z =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
- 3 Variable Systems of Equations – Substitution Method
- 3 Variable Systems of Equations – Elimination Method