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Equations and greatest common divisor

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(1) 234x+539y=1
(2) 875x+235y=10

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Solution Summary

This shows how to solve two equations by finding the greatest common divisor.

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(1) 234x+539y=1
(2) 875x+235y=10

(1) x= -205, y=89
Solution:
539 = 234*2 + 71 gcd(234, 539) = gcd(234, 71)
234 = 71*3 + 21 gcd(234, 71) = gcd(71, 21)
71 = 21*3 + 8 gcd(71, 21) = gcd(21, 8)
21= 8*2+ 5 gcd(21, 8) = gcd(8, 5)
8 = 5*1 +3 gcd(8,5) = ...

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