# How do solve the following linear system?: -2x + 3y = -19 , x+2y =2 ?

Jan 13, 2016

The solution for the system of equations is
color(blue)(x=44/7, y=-15/7

#### Explanation:

$\textcolor{b l u e}{- 2 x} + 3 y = - 19$.........equation $\left(1\right)$

$x + 2 y = 2$, multiplying by $2$
$\textcolor{b l u e}{2 x} + 4 y = 4$.......................equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$

$\cancel{\textcolor{b l u e}{- 2 x}} + 3 y = - 19$

$\cancel{\textcolor{b l u e}{2 x}} + 4 y = 4$

$7 y = - 15$

color(blue)(y = -15/7

Finding $x$ from equation $2$
$x + 2 y = 2$

$x = 2 - 2 y$

$x = 2 - 2 \times \left(- \frac{15}{7}\right)$

$x = 2 + \frac{30}{7}$

$x = \frac{14}{7} + \frac{30}{7}$

color(blue)(x = 44/7