Answer:
x = 4, y = - 3
Step-by-step explanation:
Using the Euclidean Algorithm
72 = 1 × 56 + 16 → (1)
56 = 3 × 16 + 8 → (2)
16 = 8 × 2 + 0 ← finish when remainder is 0
Hence gcd of 56 and 72 is 8
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From (2)
8 = 1 × 56 - 3 × 16 → use (1) to replace 16
8 = 1 × 56 - 3(72 - 1 × 56 )
= 1 × 56 - 3 × 72 + 3 × 56
= 4 × 56 - 3 × 72
[ which is in the form 56x + 72y ]
with x = 4 and y = - 3
