Abstract
Many problems in business and engineering require the solution of systems of equations and inequalities. In fact, systems of linear equations and inequalities occur with such frequency that mathematicians and computer scientists have devoted considerable energy to devising methods for their solution. With the aid of large-scale computers, it is possible to solve systems involving thousands of equations or inequalities, a task that previous generations would not have dared tackle. This chapter presents the methods of substitution and elimination, methods that are applicable to all types of systems. The chapter describes graphical methods for solving systems of linear inequalities and applying this technique to linear programming problems, a type of optimization problem. Matrices and determinants provide neat schemes for automating the computational procedures for solving systems of linear equations.
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