# Chapter 7: Solving Systems of Equations and Inequalities

## Introduction

Up until this point, you’ve solved single equations and inequalities for one unknown, but what if you had more than one equation or inequality with the same but multiple unknowns? For example, what if you wanted to find the number of paid adults AND the number of paid children at a movie premiere? How could you find the value of both variables? This chapter will teach you how to do so by introducing you to systems of equations and inequalities.

A system is nothing more than a set of equations or inequalities with the same variables. To solve such systems, you can use various methods including graphing, substitution, and elimination.

## Chapter Outline

- 7.1. Graphs of Linear Systems
- 7.2. Systems Using Substitution
- 7.3. Mixture Problems
- 7.4. Linear Systems with Addition or Subtraction
- 7.5. Linear Systems with Multiplication
- 7.6. Comparing Methods for Solving Linear Systems
- 7.7. Consistent and Inconsistent Linear Systems
- 7.8. Determining the Type of Linear System
- 7.9. Applications of Linear Systems
- 7.10. Systems of Linear Inequalities
- 7.11. Linear Programming

### Chapter Summary

## Summary

This chapter focuses on solving systems of linear equations. First it provides strategies for determining if an ordered pair is a solution to a system. It then moves into methods to solve such systems, including graphing, substitution, and elimination through addition, subtraction, and multiplication. The chapter then distinguishes between dependent, consistent, and inconsistent linear systems. Systems of linear inequalities are addressed as well. Finally, it ends with an overview of linear programming, or the mathematical process of analyzing a system of inequalities to make the best decisions given the constraints of the situation