# How do you solve the following system?:  2x - y = 5 , x + 2y = 3

Jan 5, 2016

The solution for the system of equations is

color(blue)(x=13/5, y=1/5

#### Explanation:

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

$x + 2 y = 3$, multiplying by $2$

$\textcolor{b l u e}{2 x} + 4 y = 6$....equation $\left(2\right)$

Solving by elimination

Subtracting equation $2$ from $1$:

$\cancel{\textcolor{b l u e}{2 x}} - y = 5$
$- \cancel{\textcolor{b l u e}{2 x}} - 4 y = - 6$

$- 5 y = - 1$

$y = \frac{- 1}{- 5}$

color(blue)(y=1/5

Finding $x$ from equation $2$

$x + 2 y = 3$

$x = 3 - 2 y$

$x = 3 - 2 \times \left(\frac{1}{5}\right)$

$x = 3 - \frac{2}{5}$

$x = \frac{15}{5} - \frac{2}{5}$

color(blue)(x =13/5