# How do you solve the following system of equations?: 2x + 15y = -4 , -2x +3y=12?

Mar 5, 2016

The solution for the system of equations is:
color(green)(x =-16/3

color(green)(y=4/9

#### Explanation:

$\textcolor{b l u e}{2 x} + 15 y = - 4$........equation $\left(1\right)$

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

Solving by elimination:

Adding equations $\left(1\right)$ and $\left(2\right)$ results in elimination of $\textcolor{b l u e}{2 x}$

$\cancel{\textcolor{b l u e}{2 x}} + 15 y = - 4$

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

$18 y = 8$

$y = \frac{8}{18}$

color(green)(y=4/9

Finding $x$ from equation $\left(1\right)$:
$2 x + 15 y = - 4$

$2 x = - 4 - 15 y$

$2 x = - 4 - 15 \times \frac{4}{9}$

$2 x = - 4 - \frac{60}{9}$

$2 x = - \frac{36}{9} - \frac{60}{9}$

$2 x = - \frac{96}{9}$

$x = - \frac{96}{18}$

color(green)(x =-16/3