The cardinality of the set of solutions to a system of congruence equations modulo a prime power is estimated by applying the Newton polyhedral method. Estimates to this value are obtained for an n-tuple of polynomials f = (fj, > • - > fn) tri coordinates x. = (Xj, . . . , xn) with coefficients in Z . The discussion is on the estimates corresponding to the polynomials f that are linear inland a specific pair of quadratics in ZJx, y].