# How do you solve 7x - 2y = -23 and 2x - 3y =-9?

Jul 6, 2017

$x = - 3$
$y = 1$

#### Explanation:

I solved the second equation for $x$, then substituted it into the first.

$2 x - 3 y = - 9$
$2 x = 3 y - 9$
$x = 1.5 y - 4.5$

$7 \left(1.5 y - 4.5\right) - 2 y = - 23$
$10.5 y - 31.5 - 2 y = - 23$
$8.5 y = 8.5$
$y = 1$

Next I substituted $y = 1$ into the second equation
$2 x - 3 \left(1\right) = - 9$
$2 x - 3 = - 9$
$2 x = - 6$
$x = - 3$

check:
$7 \left(- 3\right) - 2 \left(1\right) = - 23$
$- 21 - 2 = - 23$
$- 23 = - 23$