# How do you solve the following system: 9x - 3y = -30, -5x + 3y= 6 ?

Dec 23, 2015

The solution for the system of equations is

color(blue)(x=-6,y=-8

#### Explanation:

$9 x \textcolor{b l u e}{- 3 y} = - 30$.....equation $\left(1\right)$

$- 5 x + \textcolor{b l u e}{3 y} = 6$.........equation $\left(2\right)$

Solving by elimination.

Adding the two equations results in elimination of color(blue)(3y

$9 x \cancel{\textcolor{b l u e}{- 3 y}} = - 30$

$- 5 x + \cancel{\textcolor{b l u e}{3 y}} = 6$

$4 x = - 24$

$x = - \frac{24}{4}$

color(blue)(x=-6

Finding $y$ by substituting $x$ in equation $1$

$9 x - 3 y = - 30$

$9 \times \left(- 6\right) - 3 y = - 30$

$- 54 - 3 y = - 30$

$- 24 = 3 y$

$y = \frac{- 24}{3}$

color(blue)(y=-8