# Elimination method

## Interactive practice questions

Consider this system of equations.

 Equation 1 $\frac{4x}{5}+\frac{3y}{5}=4$4x5​+3y5​=4 Equation 2 $8x-3y=5$8x−3y=5

Which operation will change the fractional coefficients to integer coefficients in this system of equations?

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D

Multiply Equation 2 by $5$5.

A

Multiply Equation 1 by $5$5.

B

Divide Equation 2 by $3$3.

C

Divide Equation 1 by $3$3.

D
Easy
Less than a minute

Consider this system of equations.

 Equation 1 $\frac{2x}{5}+\frac{3y}{5}=-\frac{7}{5}$2x5​+3y5​=−75​ Equation 2 $-\frac{1}{4}\left(-5x+\frac{7y}{9}\right)=2$−14​(−5x+7y9​)=2

Consider the following system of equations.

 Equation 1 $3x+7y=-6$3x+7y=−6 Equation 2 $2x-y=-17$2x−y=−17

Suppose we want to solve this system by using the elimination method and eliminating $y$y.

Consider the following system of equations.

 $-8x$−8x $-$− $y$y $=$= $0$0 $-5x$−5x $+$+ $3y$3y $=$= $6$6

Suppose we solve this system using the elimination method by multiplying both sides of the first equation by $3$3 and then adding the resulting equation to the second equation. What equation do we get?

Do not solve the equation.

### Outcomes

#### 10D.AG1.01

Solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination