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The algebraic solution to systems of linear equations involving an interval square matrix and an interval right-hand side vector in terms of interval arithmetic is discussed. The basic concepts of interval arithmetic are given in a form suitable for our study. An iterative Jacobi type method is formulated and its convergence has been proved, under certain conditions on the interval matrix. In the special case when only the right-hand side is interval-valued we reduce the problem to two ordinary linear systems. An iterative numerical algorithm is proposed and numerically demonstrated.