# The sum of two integers is 41, and their difference is 15. How do you find the integers?

May 9, 2018

$13$ and $28$

#### Explanation:

I'm going to give the first integer the variable $x$, and the second integer the variable $y$.

Based on the given information, these are the resulting equations:

$x + y = 41$ (The sum of two integers is 41)

$x - y = 15$ (Their difference is 15)

I'm going to rearrange the second equation and substitute it into the first one:

$x - y = 15$

$x = 15 + y$

Now substitute:

$x + y = 41$

$\left(15 + y\right) + y = 41$

$15 + 2 y = 41$

$2 y = 26$

$y = 13$

Now substitute that into another equation to solve for $x$:

$x = 15 + y$

$x = 15 + 13$

$x = 28$