Find integers a and b such that $6=67a+25b$.
The first thing I tried was recognizing this equation as a Diophantine Equation, but is there another way to determine integers a and b without utilizing the method of Diophantine Equations? I also tried to rewrite the given equation as: $6=(a+b)+6(11a+4b)$ and took cases, but didn't obtain integer values for a and b. This problem is from a chapter that deals with Working Backwards.