# How do you solve the system of equations: 5x - 2y = 23 ; 5x + 2y = 17?

Aug 14, 2015

The solutions are
color(blue)(x=4,y=-3/2

#### Explanation:

$5 x - \textcolor{b l u e}{2 y} = 23$.........equation $\left(1\right)$
$5 x + \textcolor{b l u e}{2 y} = 17$.......equation $\left(2\right)$

Solving through elimination.
Adding the equations results in elimination of color(blue)(2y:
$5 x - \cancel{\textcolor{b l u e}{2 y}} = 23$
$5 x + \cancel{\textcolor{b l u e}{2 y}} = 17$

$10 x = 40$
color(blue)(x=4

Now finding $y$ from equation $1$

$5 x - 2 y = 23$

$5 x - 23 = 2 y$

$20 - 23 = 2 y$
$- 3 = 2 y$

color(blue)(y=-3/2