# How do you solve the following system: x + 4y = -2 , 5x - 7y = 12 ?

Dec 9, 2015

The solution for the system of equations is

color(blue)(x=-142/27, y=22/27

#### Explanation:

$x + 4 y = - 2$, multiplying the equation by $5$
$\textcolor{b l u e}{5 x} + 20 y = - 10$....equation $\left(1\right)$

$\textcolor{b l u e}{5 x} - 7 y = 12$.............equation $\left(2\right)$

Solving by elimination :

Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{5 x}} + 20 y = - 10$

$\cancel{\textcolor{b l u e}{- 5 x}} + 7 y = - 12$

$27 y = - 22$

color(blue)(y=22/27

Finding $x$ by substituting $y$ in equation $1$:
$x + 4 y = - 2$

$x = - 2 - 4 y$

$x = - 2 - 4 \cdot \left(\frac{22}{27}\right)$

$x = - 2 - \left(\frac{88}{27}\right)$

$x = - \frac{54}{27} - \left(\frac{88}{27}\right)$

color(blue)(x=-142/27