Elimination Method 3
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
 1
 2
 3
 4
 5
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
 1
 2
 3
 4
 5
 Answered
 Review

Question 1 of 5
1. Question
Solve the following systems of equations by elimination.`2x+3y=3``4x2y=14`
`x=` (3)`y=` (1)
Hint
Help VideoCorrect
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` `=` `3` Equation `1` `4x2y` `=` `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`.`4x2y` `=` `14` `` `(4x+6y)` `=` `6` `8y` `=` `8` `4x4x` 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.`4x2``y` `=` `14` Equation `2` `4x2``(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` 

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
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.`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` `6x6x` 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` 

Question 3 of 5
3. Question
Solve the following systems of equations by elimination.`3x+5y=6``3x2y=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` `3x2y` `=` `1` Equation `2` Next, subtract equation `2` from equation `1`.`3x+5y` `=` `6` `` `(3x2y)` `=` `1` `7y` `=` `7` `3x3x` 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` 

Question 4 of 5
4. Question
Solve the following systems of equations by elimination.`5x+2y=3``10x4y=6`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.`5x+2y` `=` `3` Equation `1` `10x4y` `=` `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`.`10x4y` `=` `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 `10x4y=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` `aa` 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` 
Quizzes
 Solve a System of Equations by Graphing
 Substitution Method 1
 Substitution Method 2
 Substitution Method 3
 Substitution Method 4
 Elimination Method 1
 Elimination Method 2
 Elimination Method 3
 Elimination Method 4
 Systems of Nonlinear Equations
 Systems of Equations Word Problems 1
 Systems of Equations Word Problems 2
 3 Variable Systems of Equations – Substitution Method
 3 Variable Systems of Equations – Elimination Method