# How do you solve x+y=7 and 2x+3y=20?

May 18, 2015

We can isolate one variable in one equation and substitute it in the other one.

Let's isolate $x$ in the first equation and then substitute it in the second one:

$x = 7 - y$

Then

$2 \left(7 - y\right) + 3 y = 20$
$14 - 2 y + 3 y = 20$
$y = 6$

If $y = 6$ and $x = 7 - y$, then $x = 7 - 6$, $x = 1$!

There you have: $x = 1$ and $y = 6$!