Solving Simultanteous Congruences

Hi:

I'm having some issues trying to figure out how to solve this:

The modulus is 20. So these are equivalent to the congruences:

3x + 5y = 6 (mod 20)

5x + 7y = 14 (mod 20)

which in turn is equivalent to these diophantine equations:

3x + 5y + 20z = 6

5x + 7y + 20z = 14

Now I'm kinda stuck on how to do this. Unless it is valid to subtract the two equations and use the euclidean algorithm on the result??

So

-2x -2y = -8

x + y = 4 and use the euclidean algorithm from here?? Idk any help is much appreciated. There isn't anything remotely close to this in my text...