# How do you solve 2x-7y=6, x+3y=2?

Mar 28, 2018

$\left(x , y\right) = \left(\frac{32}{13} , - \frac{2}{13}\right)$

#### Explanation:

$x = 2 - 3 y$ using the second equation, define x in terms of y
$2 \left(2 - 3 y\right) - 7 y = 6$ plug the above into the first equation
$4 - 6 y - 7 y = 6$ distribute
$4 - 13 y = 6$
$13 y = - 2$
$y = - \frac{2}{13}$
Going back to the first equation, we can plug this value in for y to achieve x.
$x = 2 - 3 \left(- \frac{2}{13}\right)$
$x = \frac{26}{13} + \frac{6}{13}$

$x = \frac{32}{13}$