mac1140_lecture14_1

mac1140_lecture14_1 - L14 9.1, 9.5 Linear and Nonlinear...

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115 L14 §9.1, 9.5 Linear and Nonlinear Sy s tem s o f Equa t ion s Definition : A linear system of equations is a set of equations, in which all the variables are at most raised to the first power. None of the variables are multiplied together. The solution set of a system of equations with two variables is all ordered pairs (, ) x y that satisfy both equations. Geometrically it represents the set of all points of intersection of the graphs of the equations. The linear system is called inconsistent if it has no solutions, that is, the graphs of the equations are parallel lines. If the system has infinitely many solutions , the equations are called dependent . The graphs of dependent equations coincide. We will consider two methods of solving systems of equations: Method of Substitution Method of Elimination
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116 Example . Solve the linear system: 57 93 2 1 x y xy + = + = Solving by Substitution:
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117 Example . Solve the linear system: 37 7 23 8 x y xy + = + = Solving by Elimination:
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This note was uploaded on 02/29/2012 for the course MAC 1140 taught by Professor Gregory during the Fall '11 term at Broward College.

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mac1140_lecture14_1 - L14 9.1, 9.5 Linear and Nonlinear...

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