# How do you solve the following system?:  -2y=2x+6 , y= 1/2x +2

May 13, 2017

$\left(x , y\right) = \left(- 3 \frac{1}{3} , \frac{1}{3}\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} - 2 y = 2 x + 6$
$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{2} x + 2$

Multiplying both sides of  by $\left(- 2\right)$
$\textcolor{w h i t e}{\text{XXX}} - 2 y = - x - 4$

Since the left sides of  and  are equal
the right sides must also be equal
$\textcolor{w h i t e}{\text{XXX}} 2 x + 6 = - x - 4$

Adding $x$ to both sides of 
$\textcolor{w h i t e}{\text{XXX}} 3 x + 6 = - 4$

Subtracting $6$ from both sides of 
$\textcolor{w h i t e}{\text{XXX}} 3 x = - 10$

Dividing both sides of  by $3$
$\textcolor{w h i t e}{\text{XXX}} x = - \frac{10}{3} \left(= - 3 \frac{1}{3}\right)$

Substituting $\left(- \frac{10}{3}\right)$ for $x$ in 
$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{2} \times \left(- \frac{10}{3}\right) + 2$

$\textcolor{w h i t e}{\text{XXXXX}} = - \frac{5}{3} + 2$

$\textcolor{w h i t e}{\text{XXXXX}} = \frac{1}{3}$

$\left(x , y\right) = \left(- \frac{10}{3} , \frac{1}{3}\right)$

The graphic solution (below) supports this result: 