The Sum of Two Numbers is 13 and Their Difference is 5

The sum of two numbers is 13 and their difference is 5. What are the two numbers? Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 13. In other words, x plus y equals 13 and can be written as equation A:

x + y = 13

The difference between x and y is 5. In other words, x minus y equals 5 and can be written as equation B:

x - y = 5

Now solve equation B for x to get the revised equation B:

x - y = 5
x = 5 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 13
5 + y + y = 13
5 + 2y = 13
2y = 8
y = 4

Now we know y is 4. Which means that we can substitute y for 4 in equation A and solve for x:

x + y = 13
x + 4 = 13
X = 9

Summary: The sum of two numbers is 13 and their difference is 5. What are the two numbers? Answer: 9 and 4 as proven here:

Sum: 9 + 4 = 13
Difference: 9 - 4 = 5

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