how to solve for this equation in $\mathbb{Z}$12
$$ [8][x]+[3][y] = [9]\\ [6][x]+[5][y]=[2] $$
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Hint: if it had a solution mod $12$ then the solution persists mod $2,\,$ where it is inconsistent.
Bill Dubuque
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See here for a simpler analogous parity contradiction, and motivation. – Bill Dubuque Oct 30 '20 at 23:44