# How do you solve the system of linear equations 4x + y = 8 and x − 2y = 2?

Mar 10, 2018

$\left(x , y\right) = \left(2 , 0\right)$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} 4 x + y = 8$
[2]$\textcolor{w h i t e}{\text{XXX}} x - 2 y = 2$

From [2], we have
[3]$\textcolor{w h i t e}{\text{XXX}} x = 2 + 2 y$

Substituting $\left(2 + 2 y\right)$ of $x$ in [1]
[4]$\textcolor{w h i t e}{\text{XXX}} 4 \left(2 + 2 y\right) + y = 8$

[5]$\textcolor{w h i t e}{\text{XXX}} 8 + 3 y = 8$

[6]$\textcolor{w h i t e}{\text{XXX}} y = 0$

Substituting $0$ for $y$ in [2]
[7]$\textcolor{w h i t e}{\text{XXX}} x - \left(2 \cdot 0\right) = 2$

[8]$\textcolor{w h i t e}{\text{XXX}} x = 2$