Question

The difference of two numbers is 7. The sum of the numbers is -1. What are the numbers? I've come up with the following equations: x-y=7 and x+y=-1. I can't seem to solve because there are no numbers on the left side of the equations. Any thoughts?

Let's call your two numbers x and y.

abs stands for absolute value.

abs(x - y) = 7
x + y = -1

Use the second equation to solve for y:

y = -1 + x

Now, plug the value for y into the first equation:

abs(x - (-1 + x)) = 7

You should be able to solve it from there.

Good luck!

Add the left and right sides of your pair of equations, like this:
x - y = 7
x + y = -1
___________
2x = 6
x = 3
y = ?
You don't need to have numbers on the left side. Just manipulate the equations so you have only x or only y on ONE side (left or right)

Leo's method, using the absolute value notation, is also correct. It will give you two pairs of answers that should be the same. In my method, consider x to be the larger number.

Thank you very much!!