# How do you solve x + y = 10  and x - y = 8?

Aug 6, 2015

$\left\{\begin{matrix}x = 9 \\ y = 1\end{matrix}\right.$

#### Explanation:

The easiest way in which you can solve this system of equations is to add the two equations to get the value of $x$.

More specifically, you add the left side of the equations and the right side of the equations separately.

$\left\{\begin{matrix}x + y = 10 \\ x - y = 8\end{matrix}\right.$

$x + \textcolor{red}{\cancel{\textcolor{b l a c k}{y}}} + x - \textcolor{red}{\cancel{\textcolor{b l a c k}{y}}} = 10 + 8$

$2 x = 18 \implies x = \frac{18}{2} = \textcolor{g r e e n}{9}$

Now use the value of $x$ in one of the two equations to get the value of $y$

$9 + y = 10 \implies y = 10 - 9 = \textcolor{g r e e n}{1}$