Precalculus: 3x3 Linear Systems of Equations

Objectives

• Students will be able to describe the effects of the coefficients of a linear function in three variables on the graph of the function.
• Students will be able to identify the number of solutions to a system of linear equations in three variables by analyzing the graphs of the equations.
• Students will be able to describe the conditions under which a system of linear equations in three variables will have 0, 1, or infinitely many solutions.

Vocabulary

• system of equations
• plane
• solution to a system of equations

About the Lesson

This lesson involves connecting graphical representations of systems of linear equations in three variables to the number of solutions of those systems.
As a result, students will:

• Manipulate a plane to observe the effect of the coefficients on the graph of the plane.
• Plot systems of two linear functions in three variables to investigate the graphical representations of solutions of a system.
• Plot systems of three linear functions in three variables to investigate the graphical representations of solutions of a system.
• Determine the number of solutions a system of linear equations in three variables can have.