New answers tagged polyhedra
1
By Farkas Lemma $Ax=b,\ x\geq 0$ is solvable if and only if $A^\top y\geq 0,\ b^\top y<0$ is not solvable.
That's the best one can do here, I don't think anything telling you individual solvability of each equation will help - especially if you know already that each individual equation is solvable.
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