# How do you solve the system of equations: 3x + 2y = 2, -2x + y = 8?

Aug 8, 2015

$\left(x , y\right) = \left(- 2 , 4\right)$

#### Explanation:

[1]$\textcolor{w h i t e}{\text{XXXX}}$$3 x + 2 y = 2$
[2]$\textcolor{w h i t e}{\text{XXXX}}$$- 2 x + y = 8$

Multiply [2] by 2
[3]$\textcolor{w h i t e}{\text{XXXX}}$$- 4 x + 2 y = 16$

Subtract [3] from [1]
[4]$\textcolor{w h i t e}{\text{XXXX}}$$7 x = - 14$

Divide by $7$
[5]$\textcolor{w h i t e}{\text{XXXX}}$$x = - 2$

Substitute $\left(- 2\right)$ for $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXXX}}$$3 \left(- 2\right) + 2 y = 2$

Simplify
[7]$\textcolor{w h i t e}{\text{XXXX}}$$y = 4$