# How do you solve the following system?:  x - y = -6, 3x+2y=12

Dec 25, 2015

#### Answer:

The solution for the system of equations is
color(blue)(x=0,y=6

#### Explanation:

$x - y = - 6$, multiplying this equation by $3$
$\textcolor{b l u e}{3 x} - 3 y = - 18$.......equation $\left(1\right)$

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

Solving by elimination.

Subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{3 x}} - 3 y = - 18$
$\cancel{- \textcolor{b l u e}{3 x}} - 2 y = - 12$

$- 5 y = - 30$

$y = \frac{30}{5}$

color(blue)(y=6

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

$x - y = - 6$

$x = - 6 + y$

$x = - 6 + 6$

color(blue)(x=0