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

Jun 25, 2018

$y = 1 , x = \frac{1}{3}$

#### Explanation:

$2 x + y = 2 - x$ and $x + 2 y = 2 + x$

Notice in the second equation you can cancel an $x$ on both sides.

$\cancel{x} + 2 y = 2 + \cancel{x}$

Therefore $y = 1$ subbing this into equation 1 gives the result

$2 x + 1 = 2 - x \rightarrow 2 x + x = 2 - 1 \rightarrow 3 x = 1 \rightarrow x = \frac{1}{3}$