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In 1921 H. Mellin [1] obtained an integral formula (in the form of Mellin-Barnes integral) for solution of general (universal) algebraic equation. He noted that integral representing the solution has a non-empty domain of convergence. The full convergence domain was found in 2007 in the article of I. A. Antipova [2]. In [3] of V. A. Stepanenko received the integral of MellinBarnes type formally representing the solution of a general system of n polynomial equations with n variables (see also [4]). Recently V.R. Kulikov [5] showed, that for n > 1 this integral can be really formal, i.e. it can have an empty domain of convergence. He has been found a necessary condition for convergence of the integral, and as a hypothesis he claimed that this condition is also sufficient for the convergence. The purpose of this work is to prove sufficiency of condition for the convergence of MellinBarnes integral representing the solution of a system of three equations with three variables. Let us consider a reduced general system of three algebraic equations  y1 1 + ∑p1 i=1 x (1) i y α (1) i 1 y β (1) i 2 y γ (1) i 3 − 1 = 0, y2 2 + ∑p2 j=1 x (2) j y α (2) j 1 y β (2) j 2 y γ (2) j 3 − 1 = 0, y3 3 + ∑p3 k=1 x (3) k y α (3) k 1 y β (3) k 2 y γ (3) k 3 − 1 = 0, (1)

On Convergence of Mellin-Barnes Integrals Representing Solutions of General Algebraic Systems of 3 Equations with 3 Variables