# How do you solve the following system?: 3x +2y = 7 , -2x - 2y = -4

Mar 14, 2016

The solution for the system of equations is:

color(green)(x=3
color(green)(y=-1

#### Explanation:

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

Solving by elimination

Adding equations $\left(1\right)$ and $\left(2\right)$ eliminates $\textcolor{b l u e}{2 y}$

$3 x + \cancel{\textcolor{b l u e}{2 y}} = 7$
$- 2 x - \cancel{\textcolor{b l u e}{2 y}} = - 4$

color(green)(x=3

Finding $y$ by substituting the value of $x$ in equation $1 :$

$3 x + 2 y = 7$

$2 y = 7 - 3 x$

2y=7-3 * color(green)(3

$2 y = 7 - 9$

$2 y = - 2$

$y = - \frac{2}{2}$

color(green)(y=-1