Is the following statement true in general (for integers a, b, c, d)? Justify your answer, referring to the definition of divisibility.

If a divides c and b divides d, then (a+b) divides (c+d).

So far what I've done is say that c=ax and d=by, where x and y are integers.

I then said that c + d = ax + by, but after this I'm not sure what to do. Any help would be greatly appreciated