# Ch 6: Algebra II: Systems of Linear Equations

### About This Chapter

## Algebra II: Systems of Linear Equations - Chapter Summary and Learning Objectives

Now that you've got a linear equations review under your belt, use this chapter to find out what happens when you need two or more linear equations to solve the same problem. Instructors teaching the video lessons help you explore linear systems' uses to compare data; they also illustrate steps for solving linear systems and comparing their graphs. This chapter is designed to teach you how to:

- Set up a system of equations to solve a word problem
- Solve systems of equations containing two or more unknowns
- Solve linear systems with infinite solutions
- Solve linear systems with no solutions

Video | Objectives |
---|---|

What Is a System of Equations? | Learn how systems of equations are used in real life. Find out how to solve a system of equations algebraically or by graphing to find the intersection point. |

How Do I Use a System of Equations? | Practice setting up a system of equations and using the substitution and elimination methods to solve it. |

How to Solve a System of Linear Equations in Two Variables | Understand how to solve a system of linear equations containing two variables. |

How to Solve a Linear System in Three Variables With a Solution | Examine steps for solving a three-variable linear system with a solution. |

How to Solve a Linear System in Three Variables With No or Infinite Solutions | Explore methods for solving a three-variable linear system with no solutions or infinite solutions. |

### 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 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.

### 3. 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.

### 4. 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.

### 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.

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### Other Chapters

Other chapters within the Algebra II: High School course

- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Homeschool Resources for High School Algebra II