Abstract
This chapter discusses a few basic methods for solving systems of linear equations. Linear equations can be solved by graphing, by elimination, by substitution, and by elimination. The method of substitution provide a unique value for x and for y if the lines intersect, result in a contradiction if the lines are parallel, and result in an identity if there is only one line. The strategy of the elimination method is to replace the original system of equations by a simpler, equivalent system that has the same solution set. The following operations are used to obtain an equivalent system: (1) an equation may be multiplied by a nonzero constant and (2) an equation may be replaced by the sum of itself and another equation. The chapter also discusses the method of Gaussian elimination, which can be extended to systems of linear equations of any size, thereby providing the basic concepts needed in the study of advanced methods for solving linear systems.
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