Discrete Math - gcd help?

Let the GCD of 4n + 7 and 5n + 9 be k.

Let A and B are integers such that
Ak = 4n + 7 and
Bk = 5n + 9.

(B - A)k
= n + 2

Thus, k divides n + 2.
Like n, n + 2 is also an arbitrary integer.
Only ±1 divides all integers, hence
k = 1.