# How do you solve the following system: 5x+2y=12, 4x-y=6 ?

Jan 2, 2016

$x = \frac{24}{23} , y = \frac{18}{13}$

#### Explanation:

By substitution

$5 x + 2 y = 12$ ---$\left(1\right)$

$4 x - y = 6$

$y = 4 x - 6$ ---$\left(2\right)$

Substitute equation $\left(2\right)$ into equation $\left(1\right)$

$5 x + 2 \left(4 x - 6\right) = 12$

$5 x + 8 x - 12 = 12$

$13 x = 24$

$x = \frac{24}{13}$

Substitute $x = \frac{24}{13}$ into equation $\left(2\right)$

$y = 4 \left(\frac{24}{13}\right) - 6$

$y = \frac{96}{13} - 6$

$y = \frac{18}{13}$

thus, $x = \frac{24}{23} , y = \frac{18}{13}$