In this article, we generalize and investigate existence of solution for infinite systems of nonlinear integral equations with two variables in a given Banach sequence space BC(R + × R + , c) using Meir-Keeler condensing and noncompactness. Validity of results are shown with the help of an illustrative example. We also introduce a coupled semi-analytic method in the case of two variables in order to construct an iteration algorithm to find a numerical solution for above-mentioned problem. The numerical results show that the produced sequence for approximating the solution in the examples is in the Banach sequence space BC(R + × R + , c) itself