# How do you solve the system y = x +4 and 2x + 3y = 22 by substitution?

May 21, 2015

You are given $y = \textcolor{red}{x + 4}$, so substitute this for the value of $y$ in
$2 x + 3 y = 22$

$2 x + 3 \textcolor{red}{\left(x + 4\right)} = 22$

$2 x + 3 x + 12 = 22$

$5 x = 10$

$x = \textcolor{b l u e}{2}$

Now substitute this value for $x$ back into $y = x + 4$
$y = \textcolor{b l u e}{2} + 4$

$y = 6$