>>854250just use the provided definition.
a = b (mod d) <=> d | (a - b) <=> ex. k s.t. dk = a - b
same with x, y:
x = y (mod d) <=> ex. l s.t. dl = x - y
To check a congruence you need to show that d divides the difference of the two parts, so start with the first:
(a + x) - (b + y) = (a - b) + (x - y) = dk + dl = d(k + l).
This implies that d divides the difference of a+x and b+y, that is by definition, a+x = b+y (mod d).
For the second you can use the same approach, but you need to properly add 0:
ax - by = ax - ay + ay - by = ...
you should be able to complete this now.
