Education Technology

3x3 Linear Systems of Equations

Activity Overview

This lesson involves connecting graphical representations of systems of linear equations in three variables to the number of solutions of those systems.

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.