The Sum of Two Numbers is 1 and Their Difference is 6

The sum of two numbers is 1 and their difference is 6. 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 6. In other words, x minus y equals 6 and can be written as equation B:

x - y = 6

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

x - y = 6
x = 6 + y

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

x + y = 1
6 + y + y = 1
6 + 2y = 1
2y = -5
y = -2.5

Now we know y is -2.5. Which means that we can substitute y for -2.5 in equation A and solve for x:

x + y = 1
x + -2.5 = 1
X = 3.5

Summary: The sum of two numbers is 1 and their difference is 6. What are the two numbers? Answer: 3.5 and -2.5 as proven here:

Sum: 3.5 + -2.5 = 1
Difference: 3.5 - -2.5 = 6

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The Sum of Two Numbers is 1 and Their Difference is 7
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