# Question #d8842

Mar 11, 2017

See the entire solution process below:

#### Explanation:

First, let's call the two numbers we are looking for $n$ and $m$.

We can then write:

$n + m = 8$

and

$n - m = 18$

First, solve the second equation for $n$:

$n - m + \textcolor{red}{m} = 18 + \textcolor{red}{m}$

$n - 0 = 18 + m$

$n = 18 + m$

Next, substitute $18 + m$ for $n$ in the first equation and solve for $m$:

$n + m = 8$ becomes:

$\left(18 + m\right) + m = 8$

$18 + m + m = 8$

$18 + 2 m = 8$

$- \textcolor{red}{18} + 18 + 2 m = - \textcolor{red}{18} + 8$

$0 + 2 m = - 10$

$2 m = - 10$

$\frac{2 m}{\textcolor{red}{2}} = - \frac{10}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} m}{\cancel{\textcolor{red}{2}}} = - 5$

$m = - 5$

Now, substitute $- 5$ for $m$ in the solution to the second equation and calculate $n$:

$n = 18 + m$ becomes:

$n = 18 + - 5$

$n = 18 - 5$

$n = 13$

The two numbers are $13$ and $- 5$