# How do you solve the following system: 2x – 4y = 8, 2x-3y=-13?

Apr 13, 2018

$x = - 38$, $y = - 21$

#### Explanation:

One of the easiest ways to solve this is by realizing that when you subtract the equations, the x's cancel and you can solve for y.
$2 x - 4 y = 8$
$- \left(2 x - 3 y = - 13\right)$

You end up with:
$- y = 21$, or $y = - 21$

Then just plug it back into one of the equations for y, like this:
$2 x - 4 \left(- 21\right) = 8$
Solve for x,
$2 x + 84 = 8$
$2 x = - 76$
$x = - 38$

You could also solve by substitution.
Start by solving one of the equations for x or y- let's solve the first one for x:
$2 x - 4 y = 8$
$2 x = 4 y + 8$
$x = 2 y + 4$
This is the same as x, right? So we can replace this for x in the second equation:
$2 \left(2 y + 4\right) - 3 y = - 13$
We've gotten rid of the x's, so we can solve for y:
$4 y + 8 - 3 y = - 13$
$y = - 21$

Now just plug this y value into one of the equations and solve for x:
$2 x - 4 \left(- 21\right) = 8$
$2 x + 84 = 8$
$2 x = - 76$
$x = - 38$