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If you divide the whole equation throughly 2 you get $$31a\equiv 19\pmod {34}$$ which you can solve to get $a\equiv 5\pmod{34}$. This then gives two possibilities for $a\pmod {68}$: either 5 or 39. For these two possibilities you can then find the corresponding $b$ (it turns out to be 5 in both cases) and check which solution works.

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