Finding and storing the set of solutions for systems of polynomial equations with parameters over finite associative (not necessarily, commutative) rings is one of basic problems in various applications connected with exploring algebraic models over these rings. In this paper, it developed unifi ed approach for presenting in implicit form the set of solutions for systems of polynomial equations with parameters over any finite associative (not necessarily, commutative) ring with unit. Proposed approach is based on notions of classes of l-associated or r-associated elements of the ring developed in the paper.