# How do you solve 3x -y = 4 and x + 2y = 13?

Dec 21, 2015

The solution for the system of equations is
color(blue)(x=3, y=5

#### Explanation:

$3 x - y = 4$, multiplying by $2$
$6 x - \textcolor{b l u e}{2 y} = 8$.....equation $1$

$x + \textcolor{b l u e}{2 y} = 13$....equation $2$

Solving by elimination

Adding equations $1$ and $2$

$6 x - \cancel{\textcolor{b l u e}{2 y}} = 8$

$x + \cancel{\textcolor{b l u e}{2 y}} = 13$

$7 x = 21$

$x = \frac{21}{7}$

color(blue)(x=3

Finding $y$ from equation $1$

$3 x - y = 4$

$3 x - 4 = y$

$3 \times \textcolor{b l u e}{3} - 4 = y$

$9 - 4 = y$

color(blue)(y=5