# Ch 5: Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Systems of Equations and Inequalities chapter of your textbook.
- Watch fun videos that cover the systems of equations and inequalities you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Solving systems of equations by graphing, substitution and elimination
- Working with three-variable systems with no or infinite solutions
- How to graph and solve a two-variable inequality
- Understanding systems of inequalities

*Explorations in Core Math Algebra 1 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. How to Solve a System of Equations by Graphing

Watch this video lesson to learn how you can solve a system of equations by graphing. Learn when you have a solution and when you don't. Also learn how easy the solution is to spot.

### 2. How to Solve a System of Equations by Substitution

Watch this video lesson to learn how you can solve a system of equations by using the substitution method. Learn the key to using the substitution method and take a quiz to practice your new skills.

### 3. How to Solve a System of Equations by Elimination

After watching this video lesson, you will have learned how to solve a system of equations by using the elimination method. You will learn what is being eliminated and how to do it so that you end with your solution.

### 4. 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.

### 5. Solving and Graphing Two-Variable Inequalities

With an inequality like y < 2x - 3, where do we start? We can look at y = 2x - 3 and graph it. We can use the graph to define all of the possible solutions.

### 6. System of Inequalities: Graphing & Concept

When we need to solve a system of two or more inequalities, we graph the solution set of each one, but we put them on the same graph and see what that looks like. The overlapping shaded areas tells us where to find the solution set.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 1: Equations
- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 3: Functions
- Explorations in Core Math Algebra 1 Chapter 4: Linear Functions
- Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis