# Chapter 5: More than One Solution to the Problem

**Advanced**Created by: CK-12

**Introduction**

In this chapter you will learn about systems of equations. You will first learn what is meant by a system of linear equations and what is meant by the solution. You will learn several methods that can be used to solve a system of linear equations. The methods that you will learn are graphing, substitution (including the comparison method), and elimination (also known as the addition and subtraction method). This chapter will concentrate on systems of linear equations.

This knowledge will then be applied to writing a system of equations for a given real-world problem and using the system to solve the problem.

You will then proceed to solving systems of linear inequalities by graphing to determine a common or feasible region. The concepts will then be applied to real-world problems to determine the best solution to the given problem.

**Lessons**

In this chapter you will do the following lessons:

- Solving Systems of Linear of Equations by Graphing
- Solving Systems of Linear Equations by Substitution
- Solving Systems of Linear Equations by Addition and Subtraction
- Real-World Applications of Systems of Linear Equations
- Solving Systems of Linear Inequalities by Graphing
- Real-World Applications of Systems of Linear Inequalities

## Chapter Outline

- 5.1. Solving Systems of Linear Equations
- 5.2. Solving Systems of Linear Equations Algebraically
- 5.3. Quiz I
- 5.4. Applications of 2 × 2 Systems of Linear Equations
- 5.5. Solving Inequalities on the Cartesian Plane
- 5.6. Solving System of Inequalities on the Cartesian Plane
- 5.7. Real-World Applications of Systems of Inequalities
- 5.8. Quiz II
- 5.9. Chapter Test