Question: The system Ax<0 is unsolvable if and only if the system yA=0, y>=0 and y!=0 is solvable.
Proof: Construct the prime dual problems
Prime:
max s min 0
st. Ax+s<=0 ==> st. Ay=0
1*y=1
if dual problem is solvable, then by strong duality, the optimal value in prime is s=0, so Ax+0<=0, but Ax<0, so prime is unsolvable.
