# The sum of two numbers is 82. Their difference is 24. How do you write a system of equations that describes this situation and solve by elimination to find the two numbers?

Sep 30, 2016

You must form equations that reflect the statement

#### Explanation:

Let's call the numbers $x$ and $y$. The statement can be written as follows:

$x + y = 82$
$x - y = 24$

Now, both equalities are true for both numbers, so we can now add the two equalities to get a third:

$x + y + x - 7 = 82 + 24$, and then

$2 x = 106$, and so $x = 53$

Now replacing $x$ by its value in either equation, say the first, we have:

$53 + y = 82$, and so $y = 82 - 53 = 29$