GCD as a linear combination

Given a and b below, use the Euclidean Algorithm to find GCD(a, b), then write the GCD(a, b) as a linear combination of a and b.

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Note: this is a typical exercise that you should be able to do, without a calculator, on a test.
You would be expected to write the details of each step, similar to the presentation shown when you click the "Get a clue" link.

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