The difference of two numbers is 3. Their sum is 13. How do you find the numbers?

Jan 6, 2017

The two numbers are $8$ and $5$.

Explanation:

Consider the two numbers as $x$ and $y$. From the given data, we write:

$x - y = 3$
$x + y = 13$

From the first equation, we determine a value for $x$.

$x - y = 3$

Add $y$ to both sides.

$x = y + 3$

In the second equation, substitute $x$ with $\textcolor{red}{\left(y + 3\right)}$.

$x + y = 13$

$\textcolor{red}{\left(y + 3\right)} + y = 13$

Open the brackets and simplify.

$\textcolor{red}{y + 3} + y = 13$

$2 y + 3 = 13$

Subtract $3$ from each side.

$2 y = 10$

Divide both sides by $2$.

$y = 5$

In the first equation, substitute $y$ with $\textcolor{b l u e}{5}$.

$x - y = 3$

$x - \textcolor{b l u e}{5} = 3$

Add $5$ to each side.

$x = 8$