# How do you solve the following system: x-5y=-9, 6x+3y=-12?

Mar 11, 2016

The solution for the system of equations is:
color(blue)(x=-29/11
color(blue)(y = 14/ 11

#### Explanation:

$x - 5 y = - 9$ , multiplying by $6$
$\textcolor{b l u e}{6 x} - 30 y = - 54$........equation $\left(1\right)$

$\textcolor{b l u e}{6 x} + 3 y = - 12$..........equation $\left(2\right)$

Solving by elimination.

Subtracting equation $\left(2\right)$ from $\left(1\right)$ results in elimination of $\textcolor{b l u e}{6 x} :$

$\cancel{\textcolor{b l u e}{6 x}} - 30 y = - 54$
$- \cancel{\textcolor{b l u e}{6 x}} - 3 y = 12$

$- 33 y = - 42$

$y = \frac{- \cancel{42}}{- \cancel{33}}$

color(blue)(y = 14/ 11

Finding $x$ from equation $1$:

$x - 5 y = - 9$

$x = - 9 + 5 y$

$x = - 9 + 5 \cdot \left(\frac{14}{11}\right)$

$x = - 9 + \frac{70}{11}$

$x = - \frac{99}{11} + \frac{70}{11}$

color(blue)(x=-29/11