# How do you solve the following system of equations?: x-2y=13 , 3x – 2y = -7?

Apr 4, 2018

$x = - 10$
$y = - \frac{23}{2}$

#### Explanation:

$x - 2 y = 13$ --- (1)
$3 x - 2 y = - 7$ --- (2)

From (1)
$x = 13 + 2 y$ --- (3)

Sub (3) into (2)

$3 \left(13 + 2 y\right) - 2 y = - 7$
$39 + 6 y - 2 y = - 7$
$4 y = - 46$
$y = - \frac{23}{2}$ --- (4)

Sub (4) into (3)
$x = 13 + 2 \left(- \frac{23}{2}\right)$
$x = - 10$