Question

Is it possible for two numbers to have a difference of 8, and a sum of -6? If so, what are the two numbers?

Answer 1

Answer: The two numbers are 1 and -7

1 minus -7 = 1 - (-7) = 1 + 7 = 8 .... difference

1 plus -7 = 1 + (-7) = -6 .... sum

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Explanation:

Let x and y be the two numbers. Let's say that x > y. Meaning that x is the bigger value.

They have a difference of 8 tells us that

x-y = 8

since "difference" is the result of subtraction. The term "sum" means the result of addition. Having a sum of -6 tells us

x+y = -6

We have this system of equations

$\begin{cases}x-y = 8\\x+y = -6\end{cases}$

We can add the equations straight down. So we add the x terms to get x+x = 2x. The y terms add to -y+y = 0y = 0, so the y terms go away. The stuff on the right hand side adds to 8+(-6) = 2

After adding the equations straight down, we boil things down to the equation 2x = 2 which solves to x = 1, after dividing both sides by 2.

Then you'll use x = 1 to find y

x-y = 8

1-y = 8

-y = 8-1

-y = 7

y = -7

or

x+y = -6

1+y = -6

y = -6-1

y = -7

Regardless of what equation you pick, you should end up with the same y value. This helps confirm we have the correct x value.

Another way to check is to plug (x,y) = (1,-7) into both equations of the system. You should end up with true statements after simplifying fully.

So the two numbers are x = 1 and y = -7