# How do you solve the system 2x = 3 - y and 2y = 12 - x by substitution?

May 25, 2015

$2 x = 3 - y$
$y = 3 - 2 x$............equation $\left(1\right)$

$2 y = 12 - x$ ........equation $\left(2\right)$

substituting equation $\left(1\right)$ in equation $\left(2\right)$
$2 \left(3 - 2 x\right) = 12 - x$
$6 - 4 x = 12 - x$
$- 6 = 3 x$
$x = - 2$

finding $y$ :
$y = 3 - 2 x$ , from equation $\left(1\right)$
$= 3 - 2 \left(- 2\right)$
$= 3 + 4 = 7$

solutions for the system of equations are
color (blue)(x=-2 and y = 7