## Solving a system of linear inequalities

Consider the following system of inequalities:

$Ax=b$; $x\geq 0$;

A is a $m\times n$ (non-square) and sparse matrix in which some part of entries are rational. How this system can be solved without using linear programming?

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 please explain what mean by "solved". – Dima Pasechnik Jul 18 at 17:35 I meant, how can the feasibility of this system be checked without using linear programming? – Star Jul 18 at 17:51 There is no general way, but perhaps you can use one of the "theorems of the alternative" such as Farkas's Lemma, Gale's Theorem, etc. – Yoav Kallus Jul 18 at 20:43 Why do you want to avoid linear programming? – Gilead Jul 18 at 20:45