# How do you solve the system x+2y=5 and 2x-2y=4?

May 26, 2015

Given
$\text{[1] } x + 2 y = 5$ and
$\text{[2] } 2 x - 2 y = 4$

By adding [1] and [2], we get
$\text{[3] } 3 x = 9$
which implies
$\text{[4] } x = 3$

Substituting [4] into [1]
$\text{[5] } 3 + 2 y = 5$
which implies
$\text{[6] } y = 1$

So the solution to the given pair of equations is
$\left(x , y\right) = \left(3 , 1\right)$