The sum of two numbers is 23. the difference of the same two numbers is 13. what are the two numbers?

18 and 5

Step-by-step explanation:

Suppose we denote the two numbers as x and y.

The problem says that the sum is 23, so:

x + y = 23

The problem also says that the difference is 13, so:

x - y = 13

We now have a system of equations:

x + y = 23

x - y = 13

Let's add these two equations together. We will get:

2x = 36 because the y's will cancel out

Divide by 2 from both sides:

x = 18

Substitute x back into one of the equations to solve for y:

x + y = 23

18 + y = 23

y = 5

So, x = 18 and y = 5.

Remove the parentheses from the equation:

Combine like terms:

The greatest common factor (GCF) of both terms is 8, so we can divide the entire expression by 8 and move it outside parentheses:

The simplified form of this expression is 8(r - 1).