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• The goal in solving a linear system of equations is to find the values of the variables that satisfy all of the equations in the system. Sometimes such values cannot be found.

• Example:

2y2x2

4yx

Solve the following system

of equations ...

Solving Linear Systems of Equations - Inconsistent Systems

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• Using the addition method we find ... 2y2x2

8y2x2

60

Such a system is called an Inconsistent System.

• Systems of three equations in three unknowns can also be inconsistent with similar algebraic results

• Since both variables were eliminated, and the result isclearly untrue, there is no solution to the system. There are no values for x and y that make both equations in the system true.

Solving Linear Systems of Equations - Inconsistent Systems

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• Using a graphing calculator to graph the two equations in the system we find ...

• Since the graphs are parallel lines, there are no points of intersection, and thus no solution points.

Solving Linear Systems of Equations - Inconsistent Systems

Table of Contents

Solving Linear Systems of Equations - Inconsistent Systems