# How do you solve the system x+y=22 and x-y=8 using substitution?

May 24, 2015

You isolate one variable in one equation and then substitute its value in the other equation. It doesn't matter which variable and equation you choose to start, as long as you substitute it in the other one.
So, in this case, let's isolate $x$ in the first one.

$x = 22 - y$

Now, let's substitute it in the second equation:

$\left(22 - y\right) - y = 8$
$- 2 y = - 14$
$y = \textcolor{g r e e n}{7}$

Now we know $y = 7$ we can go back to the value we'd found for $x$:

$x = 22 - y = 22 - 7 = \textcolor{g r e e n}{15}$