# How do you solve x+y=15 and x-y=-3?

Apr 29, 2016

Add the two equations, solve for X, and then solve either equation for y. Answer: x=6, y=9

#### Explanation:

When faced with a system of equations in two variables (x and y here), one solves it by attempting to solve for each variable one at a time. Since we know that $x - y = - 3$, we know that if we add $- 3$ to one side, we can add $x - y$ to the other, and vice versa. Thus, we will essentially "add" the two equations to one another:

$x + y + \left(x - y\right) = 15 + \left(- 3\right) \implies 2 x = 12 \implies x = 6$

Now that we have X, we plug it into our equations to find y. Technically we only need to plug it into one, but plugging it in both helps check our work:
$x + y = 15 \implies 6 + y = 15 \implies y = 9$
$x - y = - 3 \implies 6 - y = - 3 \implies y = 9$

Thus, our solution is $x = 6 , y = 9$