I'm trying to work my way through Basic Mathematics by Serge Lang and am already stuck on page 11!

The part I'm stuck at goes:

I think I can somewhat see the reasoning behind this. If the negation of expression a is equal to expression b, then expression a without the negation, added to expression b, will be 0.-(a + b) = -a - b

Proof. Remember that if x, y are integers then x = -y and y = -x mean that x + y = 0. Thus to prove our assertion, we must show that

(a + b) + (-a - b) = 0

What I'm having trouble understanding is what he means by x and y in this particular case. Does he mean the two expressions? If so, can somebody please point out how the expressions map to x and y?

Thanks.