1993•Unpublished venueRequires access
Simultaneous Equations
Clifford E. Swartz
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Abstract
Simultaneous equations is the name given to any set of equations that all have to be satisfied by the same set of values for the variables. This is a very broad definition, but in fact the major type consists of two or more variables in a linear combination: ak1x1 + ak2x2 + ⋯ + akkxk = b. In general, if there are n variables, it takes n and only n linearly independent equations of this form to obtain a unique solution, i.e., obtain only one value for each variable. Linearly independent means none of the equations can be made up by adding or subtracting some of the others to themselves or other equations any number of times.