# How do you solve 3x - 4y = -30 and 7x + 4y = 10?

Jan 13, 2016

The solution for the system of equations is
color(blue)(x=-2, y=6

#### Explanation:

$3 x - \textcolor{b l u e}{4 y} = - 30$.....equation $\left(1\right)$
$7 x + \textcolor{b l u e}{4 y} = 10$...........equation $\left(2\right)$

Solving by elimination

Adding equations $1$ and $2$

$3 x - \cancel{\textcolor{b l u e}{4 y}} = - 30$

$7 x + \cancel{\textcolor{b l u e}{4 y}} = 10$

$10 x = - 20$

$x = - \frac{20}{10}$

color(blue)(x = -2

Finding $y$ from equation $1$:

$3 x - 4 y = - 30$

$3 \times \left(- 2\right) - 4 y = - 30$

$- 6 - 4 y = - 30$

$- 6 + 30 = 4 y$

$24 = 4 y$

color(blue)(y =6