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) About Me  (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:

69x+%2B+49y+=+5

This can be rewritten as 49%28x%2By%29+%2B+20x+=+5. It follows that x+y ≡ 0 (mod 5). Suppose that x+y = 5. If this is so, 49%285%29+%2B+20x+=+5 --> 20x+=+-48%285%29 --> x = -12. Replacing x, we obtain y = 17. It checks that 966(-12) + 686(17) = 70.