15x+17y=143 where x and y are positive integers. This is a linear diophantine equation. For the purposes of HSC guess and check works. However the way we solve these types of equations is as follows:
Take the euclidean algorithm to find gcd(15,17):
17 = 15(1) + 2
15 = 2(7) + 1
2 = 1(2) + 0
So...