Elimination Method 2
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Question 1 of 5
1. Question
Solve the following systems of equations by elimination.`3x+y=5``x+y=3`
`x=` (1)`y=` (2)
Hint
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Well Done!
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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.`3x+y` `=` `5` Equation `1` `x+y` `=` `3` Equation `2` Next, subtract equation `2` from equation `1`.`3x+y` `=` `5` `` `(x+y)` `=` `3` `2x` `=` `2` `yy` cancels out Solve for `x` from the difference.`2x` `=` `2` `2x``div2` `=` `2``div2` Divide both sides by `2` `x` `=` `1` Now, substitute the value of `x` into any of the two equations.`x` `+y` `=` `3` Equation `2` `1` `+y` `=` `3` `x=1` `1+y` `1` `=` `3` `1` Subtract `1` from both sides `y` `=` `2` `x=1, y =2` 

Question 2 of 5
2. Question
Solve the following systems of equations by elimination.`5x+y=6``x+2y=24`
`x=` (4)`y=` (14)
Hint
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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+y` `=` `6` Equation `1` `x+2y` `=` `24` Equation `2` Multiply Equation `1` by `2`.`5x+y` `=` `6` `(5x+y)``xx 2` `=` `6``xx 2` `10x+2y` `=` `12` Simplify Next, Subtract equation `2` from the transformed equation.`10x+2y` `=` `12` `x+2y` `=` `24` `9x` `=` `36` `2y2y` cancels out Solve for `x`.`9x` `=` `36` `x` `=` `4` Divide both sides by `9` Now, substitute the value of `x` into any of the two equations.`x``+2y` `=` `24` Equation `2` `4``+2y` `=` `24` `x=4` `4+2y``+4` `=` `24``+4` Add `4` to both sides `2y` `=` `28` `y` `=` `14` Divide both sides by `2` `x=4, y =14` 

Question 3 of 5
3. Question
Solve the following systems of equations by elimination.`3a4b=24``4a2b=12`
`a=` (0)`b=` (6)
Hint
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Fantastic!
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In the elimination method you either add or subtract the equations to get the value of `a` and `b`First, label the two equations `1` and `2` respectively.`3a4b` `=` `24` Equation `1` `4a2b` `=` `12` Equation `2` Multiply Equation `2` by `2`.`4a2b` `=` `12` `(4a2b)``xx 2` `=` `12``xx 2` `8a4b` `=` `24` Simplify Subtract equation `1` from the transformed equation.`8a4b` `=` `24` `3a4b` `=` `24` `5a` `=` `0` `4b(4b)` cancels out Solve for `a`.`5a` `=` `0` `a` `=` `0` Divide both sides by `5` Now, substitute the value of `a` into any of the two equations.`3``a``4b` `=` `24` Equation `1` `3``(0)``4b` `=` `24` `a=0` `4b` `=` `24` `b` `=` `6` Divide both sides by `4` `a=0, b=6` 

Question 4 of 5
4. Question
Solve the following systems of equations by elimination.`a5b=8``2a3b=9`
`x=` (3)`y=` (1)
Hint
Help VideoCorrect
Excellent!
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.`a5b` `=` `8` Equation `1` `2a3b` `=` `9` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`a5b` `=` `8` Equation `1` `(a5b)``times2` `=` `8``times2` Multiply the values of both sides by `2` `2a10b` `=` `16` Equation `3` Then, subtract equation `2` from equation `3`.`2a10b` `=` `16` `` `(2a3b)` `=` `9` `7b` `=` `7` `2a2a` cancels out Solve for `b` from the difference.`7b` `=` `7` `7b``div(7)` `=` `7``div(7)` Divide both sides by `7` `b` `=` `1` Now, substitute the value of `b` into any of the two equations.`a5` `b` `=` `8` Equation `1` `a5` `(1)` `=` `8` `b=1` `a+5` `5` `=` `8` `5` Subtract `5` from both sides `a` `=` `3` `a=3, y =1` 

Question 5 of 5
5. Question
Solve the following systems of equations by elimination.`3x5y=11``2xy=5`
`x=` (2)`y=` (1)
Hint
Help VideoCorrect
Keep Going!
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.`3x5y` `=` `11` Equation `1` `2xy` `=` `5` Equation `2` Next, multiply the values of equation `2` by `5` and label the product as equation `3`.`2xy` `=` `5` Equation `2` `(2xy)``times5` `=` `5``times5` Multiply the values of both sides by `5` `10x5y` `=` `25` Equation `3` Then, subtract equation `1` from equation `3`.`10x5y` `=` `25` `` `(3x5y)` `=` `11` `7x` `=` `14` `5y(5y)` cancels out Solve for `x` from the difference.`7x` `=` `14` `7x``div7` `=` `14``div7` Divide both sides by `7` `x` `=` `2` Now, substitute the value of `x` into any of the two equations.`3``x` `5y` `=` `11` Equation `1` `3``(2)` `5y` `=` `11` `x=2` `65y` `6` `=` `11` `6` Subtract `6` from both sides `5y` `div(5)` `=` `5` `div(5)` Divide both sides by `5` `y` `=` `1` `x=2, y =1` 
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