1. Systems of Equations and Inequalities
Chapter 4
Systems of Equations and Inequalities

2. Chapter Sections
4.1 – Solving Systems of Linear Equations in Two Variables
4.2 – Solving Systems of Linear Equations in Three Variables
4.3 – Systems of Linear Equations: Applications and Problem Solving
4.4 – Solving Systems of Equations Using Matrices
4.5 – Solving Systems of Equations Using Determinants and Cramer’s Rule
4.6 – Solving Systems of Linear Inequalities
Chapter 1 Outline

3. Solving Systems of Linear Inequalities
§ 4.6
Solving Systems of Linear Inequalities

4. Solving Systems of Linear Inequalities
To Solve a System of Linear Inequalities
Graph each inequality on the same axes. The solution is the set of points whose coordinates satisfy all the inequalities in the system.
Example:
Determine the solution to the set of linear inequalities.
Continued.

5. Solving Systems of Linear Inequalities
Example continued:
Graph the inequalities.

6. Graph Linear Programming Constraints
Linear programming is a mathematical process of maximizing or minimizing the quantity subject to several limiting factors.
In a linear programming problem, the limiting factors can be represented by linear inequalities, called constraints.

7. Solve Systems of Linear Inequalities Containing Absolute Value
Solving Absolute Value Inequalities
If |x| < a and a > 0, then –a < x < a.
If |x| > a and a > 0, then x < -a or x > a.
Example Graph |x| < 3 in the Cartesian coordinate system.