Elimination Method 3
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Question 1 of 5
1. Question
Solve the following systems of equations by elimination.`2x+3y=3``4x-2y=14`-
`x=` (3)`y=` (-1)
Hint
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Correct!
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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.`2x+3y` `=` `3` Equation `1` `4x-2y` `=` `14` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`2x+3y` `=` `3` Equation `1` `(2x+3y)``times2` `=` `3``times2` Multiply the values of both sides by `3` `6x+9y` `=` `6` Equation `3` Then, subtract equation `3` from equation `2`.`4x-2y` `=` `14` `-` `(4x+6y)` `=` `6` `-8y` `=` `8` `4x-4x` 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.`4x-2``y` `=` `14` Equation `2` `4x-2``(-1)` `=` `14` `y=-1` `4x+2` `-2` `=` `14` `-2` Subtract `2` from both sides `4x` `div4` `=` `12` `div4` Divide both sides by `4` `x` `=` `3` `x=3, y =-1` -
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Question 2 of 5
2. Question
Solve the following systems of equations by elimination.`3x+2y=8``6x+8y=20`-
`x=` (2)`y=` (1)
Hint
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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.`3x+2y` `=` `8` Equation `1` `6x+8y` `=` `20` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`3x+2y` `=` `8` Equation `1` `(3x+2y)``times2` `=` `8``times2` Multiply the values of both sides by `3` `6x+4y` `=` `16` Equation `3` Then, subtract equation `3` from equation `2`.`6x+8y` `=` `20` `-` `(6x+4y)` `=` `16` `4y` `=` `4` `6x-6x` cancels out Solve for `y` from the difference.`4y` `=` `4` `4y``div4` `=` `4``div4` Divide both sides by `4` `y` `=` `1` Now, substitute the value of `y` into any of the two equations.`6x+8``y` `=` `20` Equation `2` `6x+8``(1)` `=` `20` `y=1` `6x+8` `-8` `=` `20` `-8` Subtract `8` from both sides `6x` `div6` `=` `12` `div6` Divide both sides by `6` `x` `=` `2` `x=2, y =1` -
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Question 3 of 5
3. Question
Solve the following systems of equations by elimination.`3x+5y=6``3x-2y=-1`Write fractions in the format “a/b”-
`x=` (1/3)`y=` (1)
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.`3x+5y` `=` `6` Equation `1` `3x-2y` `=` `-1` Equation `2` Next, subtract equation `2` from equation `1`.`3x+5y` `=` `6` `-` `(3x-2y)` `=` `-1` `7y` `=` `7` `3x-3x` cancels out Solve for `y` from the difference.`7y` `=` `7` `7y``div7` `=` `7``div7` Divide both sides by `7` `y` `=` `1` Now, substitute the value of `y` into any of the two equations.`3x+5``y` `=` `6` Equation `1` `3x+5``(1)` `=` `6` `y=1` `3x+5` `-5` `=` `6` `-5` Subtract `5` from both sides `3x` `div3` `=` `1` `div3` Divide both sides by `3` `x` `=` `1/3` `x=1/3, y =1` -
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Question 4 of 5
4. Question
Solve the following systems of equations by elimination.`5x+2y=-3``-10x-4y=6`Hint
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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.`5x+2y` `=` `-3` Equation `1` `-10x-4y` `=` `6` Equation `2` Next, multiply the values of equation `1` by `2` and label the product as equation `3`.`5x+2y` `=` `-3` Equation `1` `(5x+2y)``times3` `=` `-3``times3` Multiply the values of both sides by `3` `10x+6y` `=` `-6` Equation `3` Next, subtract equation `3` from equation `2`.`-10x-4y` `=` `6` `-` `(10x+4y)` `=` `-6` Applying the rule of subtracting integers where we change the signs of each value on the subtrahend, we will be getting `-10x-4y=6` as the subtrahend, which is the same as equation `2`.If the systems of equations have the same linear equations, there will be infinite solutions.`\text(Infinite Solutions)` -
Question 5 of 5
5. Question
Solve the following systems of equations by elimination.`a/4+b=6``a/6+2b=8`-
`a=` (12)`b=` (3)
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.`a/4+b` `=` `6` Equation `1` `a/6+2b` `=` `8` Equation `2` Next, multiply the values of equation `1` by `4` and label the product as equation `3`.`a/4+b` `=` `6` Equation `1` $$\left(\frac{a}{4}+b\right)\color{#CC0000}{\times4}$$ `=` `6``times4` Multiply the values of both sides by `4` to cancel the fraction `a+4b` `=` `24` Equation `3` Also multiply the values of equation `2` by `6` and label the product as equation `4`.`a/6+2b` `=` `8` Equation `2` $$\left(\frac{a}{6}+2b\right)\color{#CC0000}{\times6}$$ `=` `8``times6` Multiply the values of both sides by `6` to cancel the fraction `a+12b` `=` `48` Equation `4` Then, subtract equation `4` from equation `3`.`a+4b` `=` `24` `-` `(a+12b)` `=` `48` `-8b` `=` `-24` `a-a` cancels out Solve for `b` from the difference.`-8b` `=` `-24` `-8b``div(-8)` `=` `-24``div(-8)` Divide both sides by `-8` `b` `=` `3` Now, substitute the value of `b` into any of the four equations.`a+4``b` `=` `24` Equation `3` `a+4``(3)` `=` `24` `b=3` `a+12` `-12` `=` `24` `-12` Subtract `12` from both sides `a` `=` `12` `a=12, b =3` -
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