We propose a strategy to obtain approsin~ ate solutions of an ovcrdctcrminecl consistent polynomial system of which we are only given an approximation. These systems will bc supposc: d to be instantiations of some polynomials Fl:... F,,.+ IE k [X,: c] on the X variables: where k CC is an effective field:. c=(xl,: x,,) arc t. hc unknowns a. ntl X is to be seen as a set, of parameters. For an arbitrary choice of A; this system is generally inconsistent. M’c first propose hypothcscs under which the set of X where the systcni is consistent is an hypcrsurfacc of the space of paramclt. clrs. In the second part, wc use t. he algorithm for gcomctric resolution given in [7] in our particular setting, to give a theoretical polynomial-time resolution algorithm.