# How do you solve the system using elimination c + 2d = -2 and -2c - 5d = 3?

Jun 8, 2015

$c + 2 d = - 2$ , multiplying this equation with $2$
$2 c + 4 d = - 4$ ..........equation $\left(1\right)$

−2c−5d=3 ...............equation $\left(2\right)$

Adding the two equations to cancel color(red)(2c

$\cancel{\textcolor{red}{2 c}} + 4 d = - 4$
$\cancel{\textcolor{red}{- 2 c}} - 5 d = 3$

$- d = - 1$
 color(red)(d=1

Substituting $d$ in the first equation to find $c$

$c = - 2 - 2 d$
$c = - 2 - 2. \left(1\right)$
color(red)( c = -4

The solutions for the system of equations are:
 color(red)( d=1, c=-4