3-3 Systems of Inequalities
Objective
To solve systems of linear inequalities
Dynamic Activity
Systems of Linear Inequalities
An inequality and a system of inequalities can each have many solutions. A solution of a system of inequalities is a solution for each inequality in the system.
Essential Understanding You can solve a system of inequalities in more than one way. Graphing the solution is usually the most appropriate method. The solution is the set of all points that are solutions of each inequality in the system.
Problem 1 Solving a System by Using a Table
Assume that g and m are whole numbers. What is the solution of the system of inequalities?
Make a table of values for g and m that satisfy the second inequality. The values for g and m must be whole numbers.
Plan
Which inequality should you use to build a table?
The first inequality has an infinite number of whole number solutions. The second one has a finite number of solutions. Use the second inequality.
If g = 0, then
If m = 0, then
| g | m |
|---|---|
| 0 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 |
| 1 | 0, 1, 2, 3, 4, 5, 6, 7 |
| 2 | 0, 1, 2, 3, 4, 5 |
| 3 | 0, 1, 2 |
| 4 | 0 |
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions