# How do you solve 5x - 3y = -20 and -3x + 6y = 12?

Sep 15, 2015

The solution is
color(blue)(x=-4, y=0

#### Explanation:

$5 x - 3 y = - 20$, multiplying this equation by $2$
$10 x - \textcolor{b l u e}{6 y} = - 40$......equation $1$

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

Solving the equation by elimination .

Adding equations $1$ and $2$ results in elimination of color(blue)(6y

$10 x - \cancel{\textcolor{b l u e}{6 y}} = - 40$
$- 3 x + \cancel{\textcolor{b l u e}{6 y}} = 12$

$7 x = - 28$

$x = - \frac{28}{7}$

color(blue)(x=-4

Substituting $x$ in equation $1$ to find $y$
$5 x - 3 y = - 20$

$5 x + 20 = 3 y$

$5 \cdot \left(- 4\right) + 20 = 3 y$

$- 20 + 20 = 3 y$

$3 y = 0$

color(blue)(y=0