# The sum of the two numbers is 12. The difference between them is 4. Find the numbers?

Jun 20, 2018

The two numbers are $8$ and $4$

#### Explanation:

Call the two numbers $x$ and $y$. The first sentence translates to $x + y = 12$, while the second sentence translates to $x - y = 4$.

From the second equation we can deduce $x = y + 4$. So, the first equation becomes

$y + 4 + y = 12 \setminus \iff 2 y + 4 = 12 \setminus \iff 2 y = 8 \setminus \iff y = 4$

Substitute this value for $y$ in one of the two equations (say the second) to get

$x - 4 = 4 \setminus \iff x = 8$