## Linear Systems in nVariables

Although graphing solutions and ifnding solutions by simple substitution is tine for systems of equations with only two variables, we need to develop other procedures to find solutions for general systems of linear equations. These procedures often involve generalizations of some of the alternative solution methods that we have already referred to: subtracting equations and multiplying equations by a constant.

As we develop these methods, we will illustrate with 3-variable systems first and then, where necessary, show the general formulation in terms of n-variables.

First, we note immediately that theorem 7.1 generalizes to «-equation systems.

Theorem 7.2 A system of n linear equations has either no solution, exactly one solution, or infinitely many solutions.

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