Proving optimality conditions for linear programming is straightforward, if one assumes that the problem is primal nondegenerate. The general case, covering degeneracy, is less straightforward. Traditionally, one makes use of either Farkas' lemma or of the simplex method with some anti-cycling scheme. In this talk, we give an elementary proof of optimality conditions for linear programming, built on a straightforward classical perturbation of the constraints. The proof does not require either the use of Farkas' lemma or the use of the simplex method. As a by-product, we also obtain a proof of Farkas' lemma.