# How do you solve x+3y=-2, 2x-y=10?

Sep 8, 2015

The solutions for the system of equations is
color(blue)(x=4, y=-2

#### Explanation:

$x + 3 y = - 2$, multiplying this equation by $2$
$\textcolor{b l u e}{2 x} + 6 y = - 4$......equation $1$

$\textcolor{b l u e}{2 x} - y = 10$.....equation $2$

Solving by elimination.

Subtracting equation $2$ from $1$ results in elimination of color(blue)(2x

$\cancel{\textcolor{b l u e}{2 x}} + 6 y = - 4$
$- \cancel{\textcolor{b l u e}{2 x}} + y = - 10$
$7 y = - 14$
color(blue)(y=-2

Finding $x$ by substituting $y$ in equation $1$
$x + 3 y = - 2$
$x + 3 \cdot \left(- 2\right) = - 2$
$x - 6 = - 2$
$x = - 2 + 6$
color(blue)(x=4