The Sum of Two Numbers is 19 and Their Difference is 7

The sum of two numbers is 19 and their difference is 7. 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 19. In other words, x plus y equals 19 and can be written as equation A:

x + y = 19

The difference between x and y is 7. In other words, x minus y equals 7 and can be written as equation B:

x - y = 7

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

x - y = 7
x = 7 + y

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

x + y = 19
7 + y + y = 19
7 + 2y = 19
2y = 12
y = 6

Now we know y is 6. Which means that we can substitute y for 6 in equation A and solve for x:

x + y = 19
x + 6 = 19
X = 13

Summary: The sum of two numbers is 19 and their difference is 7. What are the two numbers? Answer: 13 and 6 as proven here:

Sum: 13 + 6 = 19
Difference: 13 - 6 = 7

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