# How do you solve using elimination of x+y=10 and x-y=2?

Nov 8, 2015

By adding the two equations together you eliminate the $y$ variable which allows you to solve $x = 6$.
Alternately, subtract one equation form the other eliminating the $x$ and allowing $y = 4$

#### Explanation:

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

Add [1] and [2]
[3]$\textcolor{w h i t e}{\text{XXX}} 2 x = 12$
$\rightarrow$[4]$\textcolor{w h i t e}{\text{XXX}} x = 6$

Subtract [2] from [1]
[5]$\textcolor{w h i t e}{\text{XXX}} 2 y = 8$
$\rightarrow$$\textcolor{w h i t e}{\text{XXX}} y = 4$