# How do you solve the system of equations 2x + 3y = 5 and x - 2y = 6?

Mar 28, 2018

$\left(x , y\right) = \left(4 , - 1\right)$

#### Explanation:

$x = 2 y + 6$ in the second equation, define x in terms of y
$2 \left(2 y + 6\right) + 3 y = 5$ plug back into the first equation
$4 y + 12 + 3 y = 5$ distribute
$7 y + 12 = 5$
$7 y = - 7$
$y = - 1$ solve for y
Then, go back to the other equation and plug this value in for y
$x = 2 \left(- 1\right) + 6$
$x = - 2 + 6$
$x = 4$