# How do you solve by substitution x + 2y = 7 and 2x + y = 8?

Jun 7, 2015

$x + 2 y = 7$
x =color(blue)( 7 - 2y ..........equation $\left(1\right)$

$2 x + y = 8$...........equation $\left(2\right)$

Substituting equation $\left(1\right)$ in $\left(2\right)$ to find $y$:
$2 \textcolor{b l u e}{\left(7 - 2 y\right)} + y = 8$
$14 - 4 y + y = 8$
$14 - 3 y = 8$
$- 3 y = - 6$
 y= 6/3 , color(purple)(y= 2

Substituting $y$ in equation $1$ to find $x$
$x = 7 - 2 y$
$x = 7 - 2.2 = 7 - 4$
color(purple)(x =3

The solution for the system of equations is
 color(purple)(x = 3 , y=2