We consider a universal trinomial system of two equations with two unknowns. The reduced variant of such a system depends on two variables a, b and its solution can be presented by hypergeometric series. We describe the convergence domain D of this series using two approaches. The first one is based on the describing the boundary of D, and the second approach is realized through the language of inequalities Delta_j(|a|,|b|)<0. The main tools of the discovery consists of the classical results of J. Horn (1889) and M. Kapranov (1991), and the notion of the amoeba for the discriminant set of the system plays an important role in the study.