About This Chapter
Linear Systems - Chapter Summary
Our instructors have developed a variety of engaging lessons you can access from home or on-the-go to boost your knowledge of linear systems. Examine the classification of linear systems and ensure you understand how problems are solved and evaluated by applying systems of equations. Once you've completed this chapter, you will be able to:
- Define a system of equations
- Classify linear systems and explain why classification is dependent on the number of solutions
- Convert a word problem into a system of equations to find an answer
- Use set notation and interval notation to express the conditions of compound inequalities
- Describe and graph the feasible region of a system of inequalities
- Evaluate parametric equations for given parameters
This chapter lets you watch the lessons in this chapter as entertaining videos with fun visual effects, or you can scroll down to access full transcripts if you'd prefer to print the lessons or read them online. Each lesson is paired with a self-assessment quiz designed to check your knowledge of the concepts it covers. Any questions that arise while studying the lessons can be submitted to our experts with ease. Use our practice exam to ensure you have a complete understanding of linear systems.
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.
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.
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.
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.
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.
6. 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.
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