Solving Inequalities and Proving Farkas' Lemma Made Easy

We present a simple algorithm that finds a nonnegative solution to a system of linear inequalities. This algorithm can be taught to secondary or college level students who have learned how to solve a system of linear equations. The algorithm is a dual version of Bland's rule for linear programming. We present a simple proof of finiteness which leads to a simple proof of Farkas' lemma.