Solve: 100y + x - 68 = 2*(100x + y)

I know the answer is x = 10; y = 21, but I did that from trial and error. Can you show me step by step how to solve this. I believe you use Euclidean Algorithm to find a gcd, and then you use the reverse Euclidean Algorithm to find a and b, such that:

d = gcd(a, b)

And then you have to use these equations:

x = x_0 + (b/d)*n AND y = y_0 - (a/d)*n

This should give a general solution, I believe.