  We have recently shown that for the special case of a bipartite system with
binary inputs and outputs there exist equalities in local theories which are
violated by quantum theory. The amount of white noise tolerated by these
equalities are twice that of inequalities. In this paper we will first
introduce an inequality in bipartite qutrits systems which, if non-maximally
entangled state is used instead of maximally entangled state, is violated more
strongly by quantum theory. Hence reproducing the results obtained in the
literature. We will then prove that our equalities in this case are violated by
quantum theory too, and they tolerate much more white noise than inequalities.
