# How do you solve the system of equations: 3x - 4y = -30, 3x+2y=6?

Aug 14, 2015

The solutions for the equations are
color(blue)(x=-2,y=6

#### Explanation:

$\textcolor{b l u e}{3 x} - 4 y = - 30$.....equation $1$
$\textcolor{b l u e}{3 x} + 2 y = 6$.............equation $2$

Solving by elimination.

Subtracting equation $2$ from $1$ results in elimination of color(blue)(3x
$\cancel{\textcolor{b l u e}{3 x}} - 4 y = - 30$
$- \cancel{\textcolor{b l u e}{3 x}} - 2 y = - 6$

$- 6 y = - 36$
color(blue)(y=6

Now we find $x$ by substituting $y$ in equation $1$
$3 x - 4 y = - 30$
$3 x = - 30 + 4 y$
$3 x = - 30 + 4 \cdot 6$
$3 x = - 30 + 24$
$3 x = - 6$
color(blue)(x=-2