# How do you solve the system of equations -2x + 4y = 6 and 2x + y = 14?

Apr 22, 2018

You could add the equations together to cancel the $- 2 x$ and the $2 x$ :

$- 2 x + 4 y = 6$
$\text{+ } 2 x + y = 14$
$\to - 2 x + 4 y + 2 x + y = 6 + 14$
$\to 5 y = 20$
$\to y = 4$

Substitute $y = 4$ into one of the two equations:

$2 x + y = 14$
$2 x + 4 = 14$
$2 x = 10$
$x = 5$