# What is the solution to the system x+y=2 and x-y=6?

Mar 6, 2018

$x = 4 \text{ and } y = - 2$

#### Explanation:

Add the two equations eliminating $y$ to solve for $x$

$\text{ } x + y = 2$
$+ x - y = 6$
$2 x + 0 y = 8$

$2 x = 8 \text{ }$ divide each side by 2

$\frac{2 x}{2} = \frac{8}{2}$

$x = 4 \text{ }$ Substitute 4 for x and solve for y

$4 + y = 2 \text{ }$ subtract 4 from each side

$4 - 4 + y = 2 - 4 \text{ }$ This gives

$y = - 2$