Elimination Method 2
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Question 1 of 5
1. Question
Solve the following simultaneous equations by elimination.`3x+y=5``x+y=3`-
`x=` (1)`y=` (2)
Hint
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Well Done!
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.`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` `y-y` 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` -
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Question 2 of 5
2. Question
Solve the following simultaneous equations by elimination.`5x+y=-6``x+2y=24`-
`x=` (-4)`y=` (14)
Hint
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Nice Job!
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+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` `2y-2y` 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` -
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Question 3 of 5
3. Question
Solve the following simultaneous equations by elimination.`3a-4b=24``4a-2b=12`-
`a=` (0)`b=` (-6)
Hint
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Fantastic!
Incorrect
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.`3a-4b` `=` `24` Equation `1` `4a-2b` `=` `12` Equation `2` Multiply Equation `2` by `2`.`4a-2b` `=` `12` `(4a-2b)``xx 2` `=` `12``xx 2` `8a-4b` `=` `24` Simplify Subtract equation `1` from the transformed equation.`8a-4b` `=` `24` `3a-4b` `=` `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` -
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Question 4 of 5
4. Question
Solve the following simultaneous equations by elimination.`a-5b=8``2a-3b=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.`a-5b` `=` `8` Equation `1` `2a-3b` `=` `9` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`a-5b` `=` `8` Equation `1` `(a-5b)``times2` `=` `8``times2` Multiply the values of both sides by `2` `2a-10b` `=` `16` Equation `3` Then, subtract equation `2` from equation `3`.`2a-10b` `=` `16` `-` `(2a-3b)` `=` `9` `-7b` `=` `7` `2a-2a` 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.`a-5` `b` `=` `8` Equation `1` `a-5` `(-1)` `=` `8` `b=-1` `a+5` `-5` `=` `8` `-5` Subtract `5` from both sides `a` `=` `3` `a=3, y =-1` -
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Question 5 of 5
5. Question
Solve the following simultaneous equations by elimination.`3x-5y=11``2x-y=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.`3x-5y` `=` `11` Equation `1` `2x-y` `=` `5` Equation `2` Next, multiply the values of equation `2` by `5` and label the product as equation `3`.`2x-y` `=` `5` Equation `2` `(2x-y)``times5` `=` `5``times5` Multiply the values of both sides by `5` `10x-5y` `=` `25` Equation `3` Then, subtract equation `1` from equation `3`.`10x-5y` `=` `25` `-` `(3x-5y)` `=` `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` `6-5y` `-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` -