This paper considers systems of linear Fredholm-Volterra integral equations using a modified homotopy analysis method (MHAM) and the Gauss-Legendre quadrature formula (GLQF) to find approximate solutions. Standard homotopy analysis method (HAM), MHAM, and optimal homotopy asymptotic method (OHAM) are compared for the same number of iterations. It is noted from the chosen examples that MHAM with GLQF is comparable with standard HAM and OHAM. In all cases, MHAM with GLQF approaches exact solutions, where residual rapidly converges to zero when the number of iterations and quadrature nodes increases. The HAM developed in this paper is better than the HAM developed by Shidfar & Molabahrami in "Solving a system of integral equations by an analytic method".