# How do you solve the system w + z = 14 and w - 2z = 2 by substitution?

May 31, 2015

$w + z = 14$
 w= color(red)(14-z......equation$\left(1\right)$
$w - 2 z = 2$.....equation $\left(2\right)$

Substituting equation $\left(1\right)$ in $\left(2\right)$
$\textcolor{red}{\left(14 - z\right)} - 2 z = 2$
$14 - 3 z = 2$
$- 3 z = - 12$
$z = \frac{12}{3} = 4$

Substituting $z$ in equation $\left(1\right)$ to find $w$
$w = 14 - z$
$w = 14 - 4 = 10$

The solution for the system of equations is
 color(blue)(z = 4, w=10