# Question #2d9fe

Jan 16, 2017

The numbers are $12 \mathmr{and} 7$

#### Explanation:

Choose variables for the two numbers first and then write two equations from the information given.

Let the numbers be $x \mathmr{and} y$, where $x > y$

Their sum is 19: $\text{ } x + y = 19. \ldots \ldots \ldots \ldots \ldots \ldots \ldots A$
The difference is 5$\text{ } x - y = 5. \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . B$

Adding the equations together will eliminate the y terms.

$A + B : \text{ "2x= 24" } \leftarrow$ divide both sides by 2

$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} x = 12$

Once you know one number, the other is easy to find:

$12 + 7 = 19 \mathmr{and} 12 - 7 = 5$

The numbers are $12 \mathmr{and} 7$