# How do you solve the system y=5x-7  and -3x-2y=-12 by substitution?

Jun 3, 2015

We know that $y = 5 x - 7$ so we are just going to replace the $y$ in the other equation :

$- 3 x - 2 y = - 12$
$- 3 x - 2 \cdot \left(5 x - 7\right) = - 12$
$- 3 x - 10 x + 14 = - 12$
$- 13 x = - 12 - 14$ ( we substract $14$ on each side )
$- 13 x = - 26$
$x = 2$ ( we divide by $- 13$ on each side )

Now that we have $x$, we can find $y$ with the first equation :

$y = 5 x - 7$
$y = 5 \cdot 2 - 7$
$y = 10 - 7$
$y = 3$