# How do you solve the system  x-2y=8 and -x+5y=-5?

Jun 10, 2015

The solution for the system of equations is:
 color(red)( x = 10 , y=1

#### Explanation:

$\textcolor{red}{x} - 2 y = 8$.....equation $\left(1\right)$
$\textcolor{red}{- x} + 5 y = - 5$ .....equation $\left(2\right)$

Adding equations $1$ and $2$ to eliminate color(red)(x
$\cancel{\textcolor{red}{x}} - 2 y = 8$
$\cancel{\textcolor{red}{- x}} + 5 y = - 5$

$3 y = 3$
color(red)(y=1

Substituting $y$ in equation $1$ to find $x$

$x = 8 + 2 y$
$x = 8 + 2 \times 1$
color(red)( x = 10