Elimination Method 4
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Question 1 of 5
1. Question
Solve the following systems of equations by elimination.`4x-3y=7``5x+2y=3`-
`x=` (1)`y=` (-1)
Hint
Help VideoCorrect
Great Work!
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.`4x-3y` `=` `7` Equation `1` `5x+2y` `=` `3` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`4x-3y` `=` `7` Equation `1` `(4x-3y)``times2` `=` `7``times2` Multiply the values of both sides by `2` `8x-6y` `=` `14` Equation `3` Also multiply the values of equation `2` by `3` and label the product as equation `4`.`5x+2y` `=` `3` Equation `2` `(5x+2y)``times3` `=` `3``times3` Multiply the values of both sides by `3` `15x+6y` `=` `9` Equation `4` Then, add equation `3` to equation `4`.`8x-6y` `=` `14` `+` `(15x+6y)` `=` `9` `23x` `=` `23` `-6x+6x` cancels out Solve for `x` from the sum.`23x` `=` `23` `23x``div23` `=` `23``div23` Divide both sides by `23` `x` `=` `1` Now, substitute the value of `x` into any of the two equations.`5``x` `+2y` `=` `3` Equation `2` `5``(1)` `+2y` `=` `3` `x=1` `5+2y` `-5` `=` `3` `-5` Subtract `5` from both sides `2y` `div2` `=` `-2` `div2` Divide both sides by `2` `y` `=` `-1` `x=1, y =-1` -
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Question 2 of 5
2. Question
Solve the following systems of equations by elimination.`2m+3n=18``4m-2n=12`Write mixed numbers in the format “a b/c”-
`x=` (4 1/2)`y=` (3)
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.`2m+3n` `=` `18` Equation `1` `4m-2n` `=` `12` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`2m+3n` `=` `18` Equation `1` `(2m+3n)``times2` `=` `18``times2` Multiply the values of both sides by `3` `4m+6n` `=` `36` Equation `3` Then, subtract equation `3` from equation `2`.`4m-2n` `=` `12` `-` `(4m+6n)` `=` `36` `-8n` `=` `-24` `4m-4m` cancels out Solve for `n` from the difference.`-8n` `=` `-24` `-8n``div(-8)` `=` `-24``div(-8)` Divide both sides by `-8` `n` `=` `3` Now, substitute the value of `n` into any of the two equations.`2m+3``n` `=` `18` Equation `1` `2m+3``(3)` `=` `18` `n=3` `2m+9` `-9` `=` `18` `-9` Subtract `9` from both sides `2m` `div2` `=` `9` `div2` Divide both sides by `2` `m` `=` `9/2` `m` `=` `4 1/2` Simplify `m=4 1/2, n =3` -
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Question 3 of 5
3. Question
Solve the following systems of equations by elimination.`6x-y=-2``-18x+3y=4`Hint
Help VideoCorrect
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.`6x-y` `=` `-2` Equation `1` `-18x+3y` `=` `4` Equation `2` Next, multiply the values of equation `1` by `3` and label the product as equation `3`.`6x-y` `=` `-2` Equation `1` `(6x-y)``times3` `=` `-2``times3` Multiply the values of both sides by `3` `18x-3y` `=` `-6` Equation `3` Next, add equation `3` from equation `2`.`-18x+3y` `=` `4` `+` `(18x-3y)` `=` `-6` `0` `=` `-2` `-18x+18x` and `3y-3y` cancel out Since both values with the `x` and `y` variables were eliminated, we cannot determine their values with this method.Therefore, these simultaneous equations have no solution.`\text(No Solution)` -
Question 4 of 5
4. Question
Solve the following systems of equations by elimination.`2x-3y=5``4x-6y=14`Hint
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Correct!
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` `=` `5` Equation `1` `4x-6y` `=` `14` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`2x-3y` `=` `5` Equation `1` `(2x-3y)``times2` `=` `5``times2` Multiply the values of both sides by `2` `4x-6y` `=` `10` Equation `3` Next, subtract equation `3` from equation `2`.`4x-6y` `=` `14` `-` `(4x-6y)` `=` `10` `0` `=` `4` `4x-4x` and `-6y-6y` cancel out Since both values with the `x` and `y` variables were eliminated, we cannot determine their values with this method.Therefore, these systems of equations have no solution.`\text(No Solution)` -
Question 5 of 5
5. Question
Solve the following systems of equations by elimination.`x+y/2=5``(x+4y)/3=4`-
`x=` (4)`y=` (2)
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.`x+y/2` `=` `5` Equation `1` `(x+4y)/3` `=` `4` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`x+y/2` `=` `5` Equation `1` $$\left(x+\frac{y}{2}\right)\color{#CC0000}{\times2}$$ `=` `5``times2` Multiply the values of both sides by `2` to cancel the fraction `2x+y` `=` `10` Equation `3` Also multiply the values of equation `2` by `3` and label the product as equation `4`.`(x+4y)/3` `=` `4` Equation `2` $$\left(\frac{x+4y}{3}\right)\color{#CC0000}{\times3}$$ `=` `4``times3` Multiply the values of both sides by `3` to cancel the fraction `x+4y` `=` `12` Equation `4` Now multiply the values of equation `4` by `2` and label the product as equation `5`.`x+4y` `=` `12` Equation `4` `(x+4y)``times2` `=` `12``times2` Multiply the values of both sides by `2` `2x+8y` `=` `24` Equation `5` Then, subtract equation `3` from equation `5`.`2x+8y` `=` `24` `-` `(2x+y)` `=` `10` `7y` `=` `14` `2x-2x` cancels out Solve for `y` from the difference.`7y` `=` `14` `7y``div7` `=` `14``div7` Divide both sides by `7` `y` `=` `2` Now, substitute the value of `y` into any of the five equations.`2x+` `y` `=` `10` Equation `3` `2x+` `(2)` `=` `10` `y=2` `2x+2` `-2` `=` `10` `-2` Subtract `2` from both sides `2x` `div2` `=` `8` `div2` Divide both sides by `2` `x` `=` `4` `x=4, y =2` -
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