# The sum of 2 numbers is 19. Their difference is 5. Find the numbers? Thanks.

Apr 11, 2018

Nice question.

#### Explanation:

So first we are told two numbers add to $19$ :

$a + b = 19$ ---(1)

And they subtract to $5$ :

$a - b = 5$ ---(2)

These are two simultaneous equation and can be solved by elimination:

(1) + (2):

$\left(a + b\right) + \left(a - b\right) = 19 + 5$

$2 a = 24$

$a = 12$

In (1):

$12 + b = 19$

$b = 7$

So the two numbers are $12$ and $7$.