Ch 19: GACE Math: Systems of Equations

About This Chapter

This chapter presents a series of short video lessons on the equations systems topics you can expect to encounter on your GACE Math certification assessment. If you have any questions about systems of equations that aren't cleared up by this material, please let our instructors know.

GACE Math: Systems of Equations - Chapter Summary

Georgia educators must be able to teach the systems of equations ideas covered by these videos. If you need additional review after watching a video, consult its transcript, which makes it easy to track down key terms and equations. Chapter topics include:

  • Two-variable linear equation system solutions
  • Three-variable solutions to linear systems
  • Augmented matrices for linear systems
  • Using determinants to solve linear equation systems
  • Non-linear equation system solutions

Try your hand at the techniques by taking the quiz following each lesson. If any of the systems of equations ideas outlined here are confusing to you, reach out to our instructors for help.

7 Lessons in Chapter 19: GACE Math: Systems of Equations
Test your knowledge with a 30-question chapter practice test
How to Solve a System of Linear Equations in Two Variables

1. How to Solve a System of Linear Equations in Two Variables

Watch this video lesson to learn how you can solve a system of linear equations in two variables by using the substitution method. Learn how easy it is to use on any linear system in two variables.

How to Solve a Linear System in Three Variables With a Solution

2. How to Solve a Linear System in Three Variables With a Solution

After watching this video lesson, you will be able to solve a linear system in three variables using the elimination method. Learn the simple operations that are needed to solve your system.

How to Solve a Linear System in Three Variables With No or Infinite Solutions

3. How to Solve a Linear System in Three Variables With No or Infinite Solutions

In this video lesson, you will learn to recognize when a linear system has no solution or an infinite number of solutions. You will also learn how to go about solving each of these types of systems.

How to Write an Augmented Matrix for a Linear System

4. How to Write an Augmented Matrix for a Linear System

Watch this video lesson to learn how you can turn your system of equations into matrix form. The matrix form is another way of writing your linear system that is sometimes easier to work with.

Solving Systems of Linear Equations in Two Variables Using Determinants

5. Solving Systems of Linear Equations in Two Variables Using Determinants

Watch this video lesson to learn how you can easily find the solution of a linear system in two variables by just using determinants. All you need to find the complete solution is to find three determinants.

Solving Systems of Linear Equations in Three Variables Using Determinants

6. Solving Systems of Linear Equations in Three Variables Using Determinants

Watch this video lesson to learn how to use Cramer's rule to help you find your solutions by finding just four determinants. Learn the numbers to use for your determinants.

Solving Non-Linear Systems of Equations

7. Solving Non-Linear Systems of Equations

Many systems of equations are non-linear, and knowing how to solve these non-linear systems is important. In this lesson, learn how to recognize and solve non-linear systems of equations.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the GACE Mathematics (522): Practice & Study Guide course

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