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Find gcd(112, 24) and show?

Find gcd(112, 24) and show that no integers x and y exist such that 112x + 24y = 2.

So far:

Let a = 112 b =24

Blah blah blah

Final:

6 = 2(8) +0

So gcd(112,24) = 8

Now the remainders I started with r1 = 16 = 112-4(24) = a-4b

And the last one I'm getting r2 = 8 = 24 - 16 = b-r1 = b-a-4b = 3b-a

When I plug it back in, it's not working. Am I making an error somewhere?

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