Ch 28: Linear Programming & Systems of Equations

About This Chapter

Enhance your understanding of how to use a system of equations, how to graph the feasible region of a system of inequalities and work with parametrics, and more. These lessons on linear programming and systems of equations can help you get ready to ace an exam or prepare for a class project.

Linear Programming & Systems of Equations - Chapter Summary

As you work through this chapter on linear programming and systems of equations, you will learn about parametric equations in applied contexts and compound inequalities. There is also information about how to use parametric equations to solve real-world problems. After completing the chapter, you should feel confident and ready to:

  • Solve a system of equations
  • Classify linear systems in math
  • Convert a word problem into a system of equations
  • Express compound inequalities
  • Graph the feasible region of a system of inequalities
  • Read coordinates and graph a given point in three dimensions
  • Use the elimination method to solve a linear system in three variables
  • Define parametric and graph parametric equations

Each lesson is concise and only takes about five minutes to complete. You can filter the course list and just go over the topics that you need to review. A brief quiz is available for each lesson to test your knowledge, and you can print the quizzes for use as worksheets.

11 Lessons in Chapter 28: Linear Programming & Systems of Equations
Test your knowledge with a 30-question chapter practice test
What is a System of Equations?

1. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

Classifying Linear Systems in Math

2. Classifying Linear Systems in Math

After watching this video lesson, you'll understand how to classify linear systems and the reasons why a linear system's classification is dependent on the number of solutions it has.

How Do I Use a System of Equations?

3. How Do I Use a System of Equations?

There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.

Set Notation, Compound Inequalities, and Systems of Inequalities

4. Set Notation, Compound Inequalities, and Systems of Inequalities

In this lesson, we'll explore the conditions of compound inequalities and learn how to express them using set notation and interval notation. Test you knowledge afterward with a short quiz.

Graphing the Feasible Region of a System of Inequalities

5. Graphing the Feasible Region of a System of Inequalities

The feasible region of a system of inequalities is the area of the graph containing the points that satisfy all the inequalities at once. Watch this lesson to learn how to graph one.

Graphing Points & Lines in Three Dimensions

6. Graphing Points & Lines in Three Dimensions

After watching this video lesson, you will know how read the three coordinates given to you and graph any given point in the three-dimensional coordinate space. Then test your knowledge with a quiz.

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

7. 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.

Parametrics: Definition & Equations

8. Parametrics: Definition & Equations

Parametrics are a special type of mathematical expression that build on traditional rectangular equations. Learn how parametric equations can be used to simplify problems, create graphs, and enhance our understanding of the behavior of those graphs.

Graphs of Parametric Equations

9. Graphs of Parametric Equations

Watch this video lesson to learn how you can go about graphing parametric equations. Learn the simplest way to graph parametric equations by eliminating the parameter.

Parametric Equations in Applied Contexts

10. Parametric Equations in Applied Contexts

Watch this video lesson to learn how you can use parametric equations to help you solve real world problems such as the path of a moving object. Learn how to form parametric equations to model the real world.

Evaluating Parametric Equations: Process & Examples

11. Evaluating Parametric Equations: Process & Examples

After watching this video lesson, you will be able to evaluate a parametric equation for any given parameter. Learn the steps involved and what the complete answer looks like.

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.
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