# Ch 9: Solving Systems of Linear Equations

### About This Chapter

## Solving Systems of Linear Equations - Chapter Summary

These lessons explain what a system of equations is and how it is used. You'll be briefed on the strategies for solving systems of linear equations in two and three variables as well as solving a system of equations with two unknowns. At the end of this chapter, you should be able to:

- Define a system of equations
- Explain the role of a system of equations
- Solve a system of linear equations in two variables
- Solve a linear system in three variables with a solution or with no or infinite solutions
- Use different methods to solve a system of equations with two unknowns
- Practice solving problems with systems of equations

These lessons are designed and taught by expert instructors. Self-assessment quizzes at the end of each lesson let you test what you've learned and see where you need further review. The jump feature in the timeline allows you to quickly find certain areas of each lesson for re-watching. The lessons also include written transcripts with key words and concepts highlighted.

### 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.

### 6. Solving a System of Equations with Two Unknowns

When you have two variables and two equations, is solving the problem four times as hard? No! Not when you use the substitution or elimination method to solve systems of equations. We'll practice both in this lesson.

### 7. Solving Problems Involving Systems of Equations

Did you ever encounter a problem where you seem to have lots of information, but still have a couple of critical numbers missing? In this lesson, we'll practice solving word problems that require us to set up systems of equations.

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### Other Chapters

Other chapters within the Accuplacer Math: Advanced Algebra and Functions Placement Test Study Guide course

- Arithmetic with Rational Expressions
- Factoring in Algebra
- Expanding Polynomials
- Manipulating Roots
- Working with Exponents & Exponential Expressions
- Solving & Graphing Linear Equations
- Quadratic Equations
- Calculating & Graphing Inequalities
- Geometric Angles & Shapes
- Line Theorems
- Similarity & Congruency in Geometry
- Pythagorean Theorem
- Graphs of Algebraic Functions
- Understanding Exponential & Logarithmic Functions
- Trigonometric Functions & Equations
- Accuplacer Math: Advanced Algebra and Functions Placement Test Flashcards