I would like some help on the problem above, it is a part of a school problem set but I'm having a bit of trouble with the explanation for it. The question is as follows:
Suppose x and y are relatively prime integers. What are all possible values for gcd(7x−y, x+ 2y)? Explain.
From what I understand, the only common prime factor between x and y has to be 1 and from trial and error, I find that the resulting gcd also seems to 1. Could anyone please help me show how this could be written out and explained? Thank you!