SOLUTION: Find integers x and y satisfying 966x + 686y = 70

SOLUTION: Find integers x and y satisfying 966x + 686y = 70

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Question 436086: Find integers x and y satisfying 966x + 686y = 70
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Note that all the coefficients are divisible by 14, so we can divide through by 14:

This can be rewritten as . It follows that x+y ≡ 0 (mod 5). Suppose that x+y = 5. If this is so, --> --> x = -12. Replacing x, we obtain y = 17. It checks that 966(-12) + 686(17) = 70.
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