# How do you solve the system 2x - 2y=5 and 5x + 2y=9?

Jun 7, 2015

$2 x - \cancel{\textcolor{b l u e}{2 y}} = 5$ ........equation $\left(1\right)$

$5 x + \cancel{\textcolor{b l u e}{2 y}} = 9$..........equation $\left(2\right)$

Adding equations $\left(1\right)$ and $\left(2\right)$ we can eliminate $\textcolor{b l u e}{2 y}$

$7 x = 9 + 5$

$7 x = 14$

color(blue)( x = 2

Substituting $x$ in equation $\left(1\right)$

$2 x - 2 y = 5$
$4 - 2 y = 5$
$4 - 5 = 2 y$
$2 y = - 1$
 color(blue)(y = -1/2

The solutions for the system of equations are:
color(blue)(x =2, y =-1/2