# How do you solve the system of equations algebraically 7x+y=9, 5x-y=15?

$\left(x , y\right) = \left(2 , - 5\right)$

#### Explanation:

We can add the two equations together to eliminate the $y$ term, solve for $x$, then substitute in. Like this:

$7 x + y = 9$
$5 x - y = 15$

$12 x \textcolor{w h i t e}{000} = 24$

$x = 2$

Substituting into either of the original equations will give us $y$ (I'll do both to show it doesn't matter):

$7 x + y = 9$

$7 \left(2\right) + y = 9$

$14 + y = 9$

$y = - 5$

~~~~~

$5 x - y = 15$

$5 \left(2\right) - y = 15$

$10 - y = 15$

$- y = 5$

$y = - 5$