# How do you solve y= -2x + 2 and 6x + 2y = 3?

Jun 18, 2018

$\left(x , y\right) = \left(- \frac{1}{2} , 3\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} y = - 2 x + 2$
[2]$\textcolor{w h i t e}{\text{XXX}} 6 x + 2 y = 3$

The form given for equation [1] makes solution by substitution the most obvious method:

Base on [1] we can substitute $\left(- 2 x + 2\right)$ for $y$ in [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 6 x + 2 \left(- 2 x + 2\right) = 3$

Simplifying [3]
[4]$\textcolor{w h i t e}{\text{XXX}} 2 x + 4 = 3$
or
[5]$\textcolor{w h i t e}{\text{XXX}} x = - \frac{1}{2}$

We can now substitute $\left(- \frac{1}{2}\right)$ for $x$ in [1]
[6]$\textcolor{w h i t e}{\text{XXX}} y = - 2 \left(- \frac{1}{2}\right) + 2 = 3$