# How do you solve the system using the elimination method for -3x+2y=-6 and 2x+2y=5?

Jul 2, 2015

The solution is:
 color(blue)(x=11/5
color(blue)( y=3/10

#### Explanation:

$- 3 x + \textcolor{b l u e}{2 y} = - 6$.......equation $\left(1\right)$

$2 x + \textcolor{b l u e}{2 y} = 5$............equation $\left(2\right)$

Subtracting equation $\left(2\right)$ from $\left(1\right)$ to eliminate color(blue)(2y

$- 3 x + \cancel{\textcolor{b l u e}{2 y}} = - 6$
$- 2 x - \cancel{\textcolor{b l u e}{2 y}} = - 5$

$- 5 x = - 11$
 color(blue)(x=11/5

Finding $y$ from equation $1$

$- 3 x + 2 y = - 6$

$2 y = - 6 + 3 x$

$y = \frac{- 6 + 3 x}{2}$

$y = \frac{- 6 + 3 \cdot \left(\frac{11}{5}\right)}{2}$

 y=(-30 +33 )/(5 * 2

color(blue)( y=3/10