# Chapter 7: Systems of Equations and Inequalities; Counting Methods

Difficulty Level:

**Basic**Created by: CK-12

James is trying to expand his pastry business to include cupcakes and personal cakes. He has a limited amount of manpower to decorate the new items and a limited amount of material to make the new cakes. In this chapter, you will learn how to solve this type of situation.

Every equation and inequality you have studied thus far is an example of a **system**. A system is a set of equations or inequalities with the same variables. This chapter focuses on the methods used to solve a system such as graphing, substitution and elimination. You will combine your knowledge of graphing inequalities to solve a system of inequalities.

Chapter Outline

- 7.1.
## Linear Systems by Graphing

- 7.2.
## Solving Systems by Substitution

- 7.3.
## Solving Linear Systems by Addition or Subtraction

- 7.4.
## Solving Linear Systems by Multiplication

- 7.5.
## Special Types of Linear Systems

- 7.6.
## Systems of Linear Inequalities

- 7.7.
## Probability and Permutations

- 7.8.
## Probability and Combinations

- 7.9.
## Chapter 7 Review

- 7.10.
## Chapter 7 Test

### Chapter Summary

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Description

This chapter introduces students to linear systems of equations and inequalities as well as probability and combinations. Operations on linear systems are covered, including addition, subtraction, multiplication, and division.

Difficulty Level:

Basic
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Date Created:

Feb 22, 2012
Last Modified:

Dec 11, 2014
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