# The sum of two numbers is 188. The difference is 54. How do you find the numbers using a system of equations?

Oct 19, 2015

I found:
$x = 121$
$y = 67$

#### Explanation:

Call your numbers $x$ and $y$ so you get:
$\left\{\begin{matrix}x + y = 188 \\ x - y = 54\end{matrix}\right.$ you can add the two equations (in columns) to get:
$2 x + 0 = 242$
$x = \frac{242}{2} = 121$ use this value into the first equation:
$121 + y = 188$
$y = 188 - 121 = 67$