Elimination Method 4
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 simultaneous 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` -
-
Question 2 of 5
2. Question
Solve the following simultaneous 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` -
-
Question 3 of 5
3. Question
Solve the following simultaneous 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 simultaneous equations by elimination.`2x-3y=5``4x-6y=14`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` `=` `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 simultaneous 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` -
Quizzes
- Solve Simultaneous 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
- Nonlinear Simultaneous Equations
- Simultaneous Equations Word Problems 1
- Simultaneous Equations Word Problems 2
- 3 Variable Simultaneous Equations – Substitution Method
- 3 Variable Simultaneous Equations – Elimination Method