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In this paper, using Banach fixed-point theorem, we study the existence and uniqueness of solution for a system of linear equations. Further, we prove the existence and uniqueness of the continuous solutions of linear and non-linear Fredholm integral equations over the Banach space . Our claim is also illustrated with the applications to respective examples for proving the existence results.doi:10.5281/zenodo.1219393 fatcat:dfzhyzysovgn5bjl4rrsul2pma