 # Table of Contents 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.

## Presentation on theme: "Table of Contents 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."— Presentation transcript:

Table of Contents 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: Solve the following system of equations... Solving Linear Systems of Equations - Inconsistent Systems

Table of Contents Slide 2 Using the addition method we find... 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 is clearly 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

Table of Contents Slide 3 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