General solution using Euclidean Algorithm  
I was able to come up with the integer solution that they also have in the textbook using the same method they used but I am really puzzled how they come up with a solution for all the possible integer combinations...how do they come up with that notation/equation that represents all the integer solutions ? I am talking about the very last line.

I solved the problem...joriki your solution is correct but I found out what I didnt know after reading some text in book....
it basically says that if you want the complete solution of an equation, you first solve for a unique solution so find an x and y that works....then take the x and add to it the integer coefficient of y/GCD *n. Take your y solution you found and subtract from it integer coefficient of x/GCD *n. That is your complete solution for all integers n
