The difference of two numbers is 1. Their sum is 9, What are the numbers?

Nov 22, 2016

$5$ and $4$

Explanation:

Let the two numbers be $x$ and $y$

$x - y = 1$
$x + y = 9$

Solve for $x$ in the first equation

$x = 1 + y$

Substitute $1 + y$ instead of $x$ in the second equation

$\left(1 + y\right) + y = 9$
$1 + 2 y = 9$
$2 y = 8$
$y = 4$

Substitute $y$ in any of the equations

$x + y = 9$
$x + 4 = 9$
$x = 5$

The two numbers are $5$ and $4$