# Which value of x satisfies both -9x + 4y = 8 and -3x − y = 4 given the same value of y?

## A.-1/7 B.-7/9 C.-8/7 D.-9 E.-4/3

Jul 25, 2018

A. $- \frac{8}{7}$

#### Explanation:

Solve the system of linear equations by elimination.

Equation 1: $- 9 x + 4 y = 8$

Equation 2: $- 3 x - y = 4$

Multiply Equation 2 by $4$.

$4 \left(- 3 x - y\right) = 4 \times 4$

$- 12 x - 4 y = 16$

$- 9 x \textcolor{w h i t e}{.} + 4 y = 8$
$- 12 x - 4 y = 16$
$- - - - - - -$
$- 21 x \textcolor{w h i t e}{\ldots \ldots . .} = 24$

$- 21 x = 24$

Divide both sides by $- 21$.

$x = - \frac{24}{21}$

Reduce by dividing the numerator and denominator by $3$.

$x = - \frac{8}{7}$