Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: College Algebra
Topic: Systems and Matrices
Subtopic: Nonlinear Systems of Equations

Overview

Our focus is to extend the algebraic and graphic methods of solving linear systems to nonlinear systems. Nonlinear systems are systems of equations that include variables to powers higher than one, negative powers on variables, non-integer powers on variables, variables in the denominator, or variables in a radicand. The graphs of nonlinear equations are, of course, not straight lines! These systems of wiggly curves may have many intersection points thus many solutions to find.

As you work through this material be sure to try solving both algebraically and graphically. When solving algebraically, concentrate on when the elimination method would work or when the substitution method is the way to go.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 5.2.1 Recognizing a system of equations as nonlinear
• 5.2.2 Solve 2x2 system of nonlinear equations algebraically using the elimination or substitution methods
• 5.2.3 Solve 2x2 system of nonlinear equations graphically using an electronic grapher
• 5.2.4 Understand the graphical significance of the Real solutions to a nonlinear system

Terminology

Terms you should be able to define: nonlinear equation, nonlinear system of equations

rev. 2020-11-29