# How do you solve the following system?: -2x+12y=-20 , x-5y=15

Apr 19, 2016

The solution for the system of equations is:
color(green)(x=40
color(green)(y= 5

#### Explanation:

$\textcolor{g r e e n}{- 2 x} + 12 y = - 20$..........equation $\left(1\right)$

$x - 5 y = 15$, multiplying by $2$
$\textcolor{g r e e n}{2 x} - 10 y = 30$....................equation $\left(2\right)$

Solving by elimination.

Adding equations $1$ and $2$ eliminates $2 x$

$\cancel{\textcolor{g r e e n}{- 2 x}} + 12 y = - 20$
$\cancel{\textcolor{g r e e n}{2 x}} - 10 y = 30$

$2 y = 10$

$y = \frac{10}{2}$

color(green)(y= 5

Finding $x$ from the second equation provided:

$\textcolor{b l u e}{x} - 5 y = 15$

$x = 15 + 5 y$

x = 15+ 5 * color(green)(5

$x = 15 + 25$

color(green)(x=40