# How do you solve the following system of equations?: x+y= -2 , x - y= 10?

Jan 28, 2016

$x = 4$
$y = - 6$

#### Explanation:

$x = - 2 - y$

subsitute $x = - 2 - y$ into $x - y = 10$

$\rightarrow - 2 - y - y = 10$

$\rightarrow - 2 - 2 y = 10$

$\rightarrow - 2 y = 12$

$y = - 6$

substitute $y = - 6$ into $x - y = 10$

$\rightarrow x - 6 - \left(- 6\right) = 10$

$\rightarrow x + 6 = 10$

$x = 4$

This is just substitution, you can also use elimination

$\rightarrow x + y = - 2$

$\rightarrow x - y = 10$

(the y's cancel each other out)

$\rightarrow 2 x = 8$

$x = 4$

substitute $x = 4$ into $x - y = 10$

$\rightarrow 4 - y = 10$

$\rightarrow - y = 6$

$y = - 6$