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

May 22, 2015

You can isolate one variable in one equation and then substitute its value in the other, as follows.

Let's, for example, isolate $y$ in the first one.

$y = 5 - 2 x$

Now, substitute it in the second:

$x - 2 \left(5 - 2 x\right) = - 5$
$x - 10 + 4 x = - 5$
$5 x = 5$
$x = 1$

Substituting this value in the $y = 5 - 2 x$,

$y = 5 - 2 \left(1\right)$
$y = 3$