Question

Are there any values of x and y for which x + y is equal to x - y

Answer 1

You can choose any value for
`x`, while you must choose
`y=0`.

Intuitively, this makes sense since
`x+y=x-y` means that you want to start from number
`x`, and you want to obtain the same result by moving left or right by
`y` units. This can't happen, unless you don't move at all, i.e.
`y=0`.

If you want to be more formal, you have

`x+y = x-y \implies x-x = -y-y \implies -2y=0 \iff y = 0`

while
`x` was canceled, so it can assume any value.