The Sum of Two Numbers is 1 and Their Difference is 1

The sum of two numbers is 1 and their difference is 1. 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 1. In other words, x plus y equals 1 and can be written as equation A:

x + y = 1

The difference between x and y is 1. In other words, x minus y equals 1 and can be written as equation B:

x - y = 1

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

x - y = 1
x = 1 + y

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

x + y = 1
1 + y + y = 1
1 + 2y = 1
2y = 0
y = 0

Now we know y is 0. Which means that we can substitute y for 0 in equation A and solve for x:

x + y = 1
x + 0 = 1
X = 1

Summary: The sum of two numbers is 1 and their difference is 1. What are the two numbers? Answer: 1 and 0 as proven here:

Sum: 1 + 0 = 1
Difference: 1 - 0 = 1

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The Sum of Two Numbers is 1 and Their Difference is 2
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