# Ch 5: Big Ideas Math Algebra 1 - Chapter 5: Solving Systems of Linear Equations

### About This Chapter

## How It Works:

- Identify the lessons in the Big Ideas Math Solving Systems of Linear Equations chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the methods of solving systems of linear equations you need to learn or review.
- Complete the quizzes 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.

## Students will learn:

- How to solve system equations by graphing, substitution and elimination
- Steps involved in solving a linear system with infinite or no solutions
- How to graph and to solve absolute value equations
- Solving two-variable inequalities
- How to graph a system of inequalities

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 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. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. Solving a System of Absolute Value Equations by Graphing

A system of absolute value equations is two more equations that contain absolute value symbols. To solve these systems you will need to find a point (x,y) or points that will work for both equations. This lesson explains how to solve these systems by graphing.

### 7. 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.

### 8. 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.

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### Other Chapters

Other chapters within the Big Ideas Math Algebra 1: Online Textbook Help course

- Big Ideas Math Algebra 1 - Chapter 1: Solving Linear Equations
- Big Ideas Math Algebra 1 - Chapter 2: Solving Linear Inequalities
- Big Ideas Math Algebra 1 - Chapter 3: Graphing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 4: Writing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 6: Exponential Functions & Sequences
- Big Ideas Math Algebra 1 - Chapter 7: Polynomial Equations & Factoring
- Big Ideas Math Algebra 1 - Chapter 8: Graphing Quadratic Functions
- Big Ideas Math Algebra 1 - Chapter 9: Solving Quadratic Equations
- Big Ideas Math Algebra 1 - Chapter 10: Radical Functions & Equations
- Big Ideas Math Algebra 1 - Chapter 11: Data Analysis & Displays