# Prove that given two equation systems can't simultaneously have solutions

I have these two equation systems. $$\ \left\{ \begin{array} {A}xA\leq b \\ x \geq 0 \end{array} \right. \quad\text{and}\quad \ \left\{ \begin{array} {A}Ay\geq 0 \\ by < 0 \\ y \geq0 \end{array} \right.$$

How to prove that when first equation has solution the second one does not have and when the second one has the first one does not have. But not simultaneously.

We have $$(xA) \le b$$, since $$y \ge 0$$,
We ahve $$(xA)y \le by$$