Jun 1, 2017

Answer: $13$ and $8$

#### Explanation:

The sum of 2 numbers is 21 and their difference is 5. Can you find the numbers?

We can write a system of equations, let $x$ and $y$ be the two numbers. Since it is given that difference between $x$ and $y$ is not zero, we can assume that one must be greater than the other, say $x > y$:
$x + y = 21$
$x - y = 5$

Now, we solve the system by elimination. We can add the equations together to eliminate the $y$ variable and solve for $x$:
$x + y + x - y = 21 + 5$
$2 x = 26$
$x = 13$

Now, we can substitute back into either of the equations to find $y$, we will use $x - y = 5$:
$13 - y = 5$

Adding $y$ to both sides and subtracting $5$ from both sides, we get:
$y = 8$

Therefore, the two numbers are $13$ and $8$