# How do you solve the following system: x = 4 – 2y , 2x-3y=-13?

Dec 13, 2015

The solution for the system of equations is

color(blue)(x=-2,y=3

#### Explanation:

x=color(blue)((4-2y)...........equation $\left(1\right)$

$2 x - 3 y = - 13$.....equation $\left(2\right)$

Solving by substitution:

$2 x - 3 y = - 13$

$2 \cdot \textcolor{b l u e}{\left(4 - 2 y\right)} - 3 y = - 13$

$8 - 4 y - 3 y = - 13$

$8 - 7 y = - 13$

$- 7 y = - 13 - 8$

$y = \frac{- 21}{- 7}$

color(blue)(y=3

Finding $x$ by substituting $y$ in equation $1$

$x = 4 - 2 y$

x=4-2 * color(blue)(3

$x = 4 - 6$

color(blue)(x=-2