# How do you solve the system 2x-9y=6 and 4x-3y=-7?

Jul 24, 2015

The solution for the system of equations is:
color(blue)(x=-27/10, y=-19/15

#### Explanation:

2x−9y=6, multiplying this equation by $2$

color(blue)(4x)−18y=12........equation $\left(1\right)$

 color(blue)(4x)−3y=−7........equation $\left(2\right)$

Solving through elimination:

Subtracting equation $\left(1\right)$ from $\left(2\right)$:
 color(blue)(cancel(4x)−3y=−7
color(blue)(cancel(-4x)+18y=-12

$15 y = - 19$

color(blue)(y=-19/15

Finding $x$ from the first equation :

2x−9y=6

$2 x = 6 + 9 y$

$x = \frac{6 + 9 y}{2}$

$x = \frac{6 + 9 \cdot \left(- \frac{19}{5}\right)}{2}$

color(blue)(x=-27/10