# How do you solve 3x-7y=-13 and -2x+3y=7?

Aug 3, 2015

The solutions for the system of equations are
color(blue)(x=-2,y=1

#### Explanation:

3x−7y=−13, Multiplying this equation with $2$
color(blue)(6x)−14y=-26......equation $\left(1\right)$

 −2x+3y=7, Multiplying this equation with $3$
 −color(blue)(6x)+9y=21.......equation $\left(2\right)$

Solving through elimination

Adding the two equations results in elimination of color(blue)(6x
cancel(6x)−14y=-26

 cancel(−6x)+9y=21

$- 5 y = - 5$
color(blue)(y=1

Now, we find $x$ by substituting $y$ in equation $\left(1\right)$
3x−7y=−13

3x−7*1=−13

3x=−13+7

$x = - \frac{6}{3}$

color(blue)(x=-2