# How do you solve x - 2y = 10 and 1/2x - 2y = 4 using substitution?

May 11, 2016

$\left(x , y\right) = \textcolor{b l u e}{12 , 1}$

#### Explanation:

Given
[1]$\textcolor{w h i t e}{\text{XXX}} x - 2 y = 10$
[2]$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} x - 2 y = 4$

We can rearrange [1] to give us an equation in terms of just $x$
[3]$\textcolor{w h i t e}{\text{XXX}} x = 2 y + 10$

This allows us to substitute $\left(2 y + 10\right)$ for $x$ in [2]
[4]$\textcolor{w h i t e}{\text{XXX}} \frac{1}{2} \left(2 y + 10\right) - 2 y = 4$

Simplifying
[5]$\textcolor{w h i t e}{\text{XXX}} y + 5 - 2 y = 4$

[6]$\textcolor{w h i t e}{\text{XXX}} - y = - 1$

[7]$\textcolor{w h i t e}{\text{XXX}} y = 1$

Now we can substitute $1$ for $y$ back in [1]
[8]$\textcolor{w h i t e}{\text{XXX}} x - 2 \left(1\right) = 10$

Simplifying
[9]$\textcolor{w h i t e}{\text{XXX}} x = 12$