Abstract: With a view to more efficiently solving system of linear inequalities, a special matrix,  imposed basis-point transition matrix, was given together with  a special negative pivoting iteration operation, by which it can be better displayed that system of linear inequalities has both linear feature and geometric-plane feature. Moreover, based on the above platform, a new solution-decision method for system of linear inequalities was proposed. With the help of this new method, the solutiondecision process of system of linear inequalities can be changed into a series of elementary column transformations of matrixes. So, this method not only works fast and simply but also can be more easily translated into programs and more efficiently accomplished on computers. In addition, a simplex locally ε regularized method was proposed so as to overcome the bad effect coming from vertex degeneration, to the vertex transition iteration processes.

Key words: system of linear inequalities, imposed basis-point transition matrix, negative pivoting iteration, locally &epsilon, regularized; , solution-decision problem