# How do you solve the system x+y=7 and 2x-y=2 by addition?

Mar 27, 2016

$\left(x , y\right) = \left(3 , 4\right)$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{x + y} = \textcolor{red}{7}$
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{2 x - y} = \textcolor{b l u e}{2}$

$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{x} + \textcolor{b l u e}{2 x} + \textcolor{red}{y} + \textcolor{b l u e}{\left(- y\right)} = \textcolor{red}{7} + \textcolor{b l u e}{2}$

$\textcolor{w h i t e}{\text{XXX}} 3 x = 9$

$\textcolor{w h i t e}{\text{XXX}} x = 3$

The we can substitute $3$ for $x$ in $\textcolor{b l u e}{2 x - y = 2}$
to get
$\textcolor{w h i t e}{\text{XXX}} 2 \left(3\right) - y = 2$

$\textcolor{w h i t e}{\text{XXX}} 6 - y = 2$

$\textcolor{w h i t e}{\text{XXX}} y = 4$