Question 436086
Note that all the coefficients are divisible by 14, so we can divide through by 14:


{{{69x + 49y = 5}}}


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