Elimination Method 1
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Question 1 of 6
1. Question
Solve the following systems of equations by elimination.`2x-3y=3``4x+3y=15`-
`x=` (3)`y=` (1)
Hint
Help VideoCorrect
Well Done!
Incorrect
In the elimination method you either add or subtract the equations to get the value of `x` and `y`First, label the two equations `1` and `2` respectively.`2x-3y` `=` `3` Equation `1` `4x+3y` `=` `15` Equation `2` Next, add the two equations.`2x-3y` `=` `3` `4x+3y` `=` `15` `6x` `=` `18` `-3y+3y` cancels out Solve for `x`.`6x` `=` `18` `x` `=` `3` Divide both sides by `6` Now, substitute the value of `x` into any of the two equations.`2``x``-3y` `=` `3` Equation `1` `2``(3)``-3y` `=` `3` `x=3` `6-3y` `=` `3` Simplify `6-3y``-6` `=` `3``-6` Subtract `6` from both sides `-3y` `=` `-3` `y` `=` `-1` `x=3, y =1` -
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Question 2 of 6
2. Question
Solve the following systems of equations by elimination.`2x-3y=8``x-y=3`-
`x=` (1)`y=` (-2)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Elimination Method
- `1)` make sure a variable has same coefficients on the 2 equations
- `2)` add or subtract the equations so that one variable is cancelled
- `3)` solve for the variable that remains
- `4)` substitute known value to one of the equations to solve for the other variable
First, label the two equations `1` and `2` respectively.`2x-3y` `=` `8` Equation `1` `x-y` `=` `3` Equation `2` Next, multiply the values of equation `2` by `2` and label the product as equation `3`.`x-y` `=` `3` Equation `2` `(x-y)``times2` `=` `3``times2` Multiply the values of both sides by `2` `2x-2y` `=` `6` Equation `3` Then, subtract equation `3` from equation `1`.`2x-3y` `=` `8` `-` `(2x-2y)` `=` `6` `-y` `=` `2` `2x-2x` cancels out Solve for `y` from the difference.`-y` `=` `2` `-y``div(-1)` `=` `2``div(-1)` Divide both sides by `-1` `y` `=` `-2` Now, substitute the value of `y` into any of the two equations.`x-` `y` `=` `3` Equation `2` `x-` `(-2)` `=` `3` `y=-2` `x+2` `-2` `=` `3` `-2` Subtract `2` from both sides `x` `=` `1` `x=1, y =-2` -
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Question 3 of 6
3. Question
Solve the following systems of equations by elimination.`5x+2y=25``4x-3y=-3`-
`x=` (3)`y=` (5)
Hint
Help VideoCorrect
Excellent!
Incorrect
In the elimination method you either add or subtract the equations to get the value of `x` and `y`First, label the two equations `1` and `2` respectively.`5x+2y` `=` `25` Equation `1` `4x-3y` `=` `-3` Equation `2` Multiply Equation `1` by `3`.`5x+2y` `=` `25` `(5x+2y)``xx 3` `=` `25``xx 3` `15x+6y` `=` `75` Simplify Multiply Equation `2` by `2`.`4x-3y` `=` `-3` `(4x-3y)``xx 2` `=` `-3``xx 2` `8x-6y` `=` `-6` Simplify Add the two transformed equations.`15x+6y` `=` `75` `8x-6y` `=` `-6` `23x` `=` `69` `6y-6y` cancels out Solve for `x`.`23x` `=` `69` `x` `=` `3` Divide both sides by `23` Now, substitute the value of `x` into any of the two equations.`5``x``+2y` `=` `25` Equation `1` `5``(3)``+2y` `=` `25` `x=3` `15+2y` `=` `25` `15+2y``-15` `=` `25``-15` Subtract `15` from both sides `2y` `=` `10` `y` `=` `5` Divide both sides by `2` `x=3, y =5` -
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Question 4 of 6
4. Question
Solve the following systems of equations by elimination.`2x-7y=19``x+2y=4`-
`x=` (6)`y=` (-1)
Hint
Help VideoCorrect
Well Done!
Incorrect
In the elimination method you either add or subtract the equations to get the value of `x` and `y`First, label the two equations `1` and `2` respectively.`2x-7y` `=` `19` Equation `1` `x+2y` `=` `4` Equation `2` Multiply Equation `1` by `2`.`2x-7y` `=` `19` `(2x-7y)``xx 2` `=` `19``xx 2` `4x-14y` `=` `38` Simplify Multiply Equation `2` by `7`.`x+2y` `=` `4` `(x+2y)``xx 7` `=` `4``xx 7` `7x+14y` `=` `28` Simplify Add the two transformed equations.`4x-14y` `=` `38` `7x+14y` `=` `28` `11x` `=` `66` `-14y+14y` cancels out Solve for `x`.`11x` `=` `66` `x` `=` `6` Divide both sides by `11` Now, substitute the value of `x` into any of the two equations.`2``x``-7y` `=` `19` Equation `1` `2``(6)``-7y` `=` `19` `x=6` `12-7y` `=` `19` `12-7y``-12` `=` `19``-12` Subtract `12` from both sides `-7y` `=` `7` `y` `=` `-1` Divide both sides by `-7` `x=6, y =-1` -
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Question 5 of 6
5. Question
Solve the following systems of equations by elimination.`2x+y=-5``4x-3y=5`-
`x=` (-1)`y=` (-3)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Elimination Method
- `1)` make sure a variable has same coefficients on the 2 equations
- `2)` add or subtract the equations so that one variable is cancelled
- `3)` solve for the variable that remains
- `4)` substitute known value to one of the equations to solve for the other variable
First, label the two equations `1` and `2` respectively.`2x+y` `=` `-5` Equation `1` `4x-3y` `=` `5` Equation `2` Next, multiply the values of equation `1` by `3` and label the product as equation `3`.`2x+y` `=` `-5` Equation `1` `(2x+y)``times3` `=` `-5``times3` Multiply the values of both sides by `3` `6x+3y` `=` `-15` Equation `3` Then, add equation `3` to equation `2`.`4x-3y` `=` `5` `+` `(6x+3y)` `=` `-15` `10x` `=` `-10` `-3y+3y` cancels out Solve for `x` from the sum.`10x` `=` `-10` `10x``div10` `=` `-10``div10` Divide both sides by `10` `x` `=` `-1` Now, substitute the value of `x` into any of the two equations.`4``x` `-3y` `=` `5` Equation `2` `4``(-1)` `-3y` `=` `5` `x=-1` `-4-3y` `+4` `=` `5` `+4` Add `4` to both sides `-3y` `div(-3)` `=` `9` `div(-3)` Divide both sides by `-3` `y` `=` `-3` `x=-1, y =-3` -
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Question 6 of 6
6. Question
Solve the following systems of equations by elimination.`2x-4y=-4``3x-2y=-10`-
`x=` (-4)`y=` (-1)
Hint
Help VideoCorrect
Exceptional!
Incorrect
Elimination Method
- `1)` make sure a variable has same coefficients on the 2 equations
- `2)` add or subtract the equations so that one variable is cancelled
- `3)` solve for the variable that remains
- `4)` substitute known value to one of the equations to solve for the other variable
First, label the two equations `1` and `2` respectively.`2x-4y` `=` `-4` Equation `1` `3x-2y` `=` `-10` Equation `2` Next, multiply the values of equation `1` by `3` and label the product as equation `3`.`2x-4y` `=` `-4` Equation `1` `(2x-4y)``times3` `=` `-4``times3` Multiply the values of both sides by `3` `6x-12y` `=` `-12` Equation `3` Also multiply the values of equation `2` by `2` and label the product as equation `4`.`3x-2y` `=` `-10` Equation `2` `(3x-2y)``times2` `=` `-10``times2` Multiply the values of both sides by `2` `6x-4y` `=` `-20` Equation `4` Then, subtract equation `4` from equation `3`.`6x-12y` `=` `-12` `-` `(6x-4y)` `=` `-20` `-8y` `=` `8` `6x-6x` cancels out Solve for `y` from the difference.`-8y` `=` `8` `-8y``div(-8)` `=` `8``div(-8)` Divide both sides by `-8` `y` `=` `-1` Now, substitute the value of `y` into any of the two equations.`2x-4``y` `=` `-4` Equation `1` `2x-4``(-1)` `=` `-4` `y=-1` `2x+4` `-4` `=` `-4` `-4` Subtract `4` from both sides `2x` `div2` `=` `-8` `div2` Divide both sides by `2` `x` `=` `-4` `x=-4, y =-1` -
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