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This article provides information on a solution for comparative static problems in which qualitative information is available but quantitative information is not. An additional property of the technique set out in the study can be incorporated directly into the system. The solution technique has been organized in the form of an algorithm, devised for maximum efficiency in use. The solution algorithm is designed to determine the sign pattern or patterns of the solution of a system of linear equations Ax = 0 where the signs of the elements of the matrix A are known but the numerical values are unspecified. The algorithm follows definite steps. The algorithm can be used to examine whether a determinant is invariant in sign with respect to changes in the numerical values of its elements.