# How do you solve for y: 2x + y = 8 , 2x - y = 8?

May 8, 2018

$y = 0$

#### Explanation:

Notice that the $y$ terms are additive inverses.
Add the two equations together to eliminate them.

$\text{ "2x+y=8" } \ldots A$
$\text{ "2x-y = 8" } \ldots B$

$A + B \text{ } 4 x = 16$

$\text{ } x = 4$

If $x = 4 , \text{ } y = 0$

We could have guessed that from looking at the equation.
In one the $y$ is added and in the other $y$ is subtracted, yet it does not affect the value of the equation at all. The only value of $y$ that would allow this to happen would be $y = 0$