Systems of Equations and Inequalities Chapter 4 Systems of Equations and Inequalities

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

Solving Systems of Linear Inequalities § 4.6 Solving Systems of Linear Inequalities

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.

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

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.

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.