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: Linear Systems of Equations

Overview

Solving linear systems algebraically by substitution or elimination methods and graphically by the intersection method should all be review from an elementary algebra course. The "review topics" list below shows topics you should remember from it. The "objectives" below list those that you should concentrate on in this college algebra course.

Review Topics (from elementary algebra)
2x2 linear systems:
Definition of linear system; what it means to be a solution to a system
Check if given values are actually a solution to a given system
Solving a 2x2 linear system by graphing manually
Solving a 2x2 linear system graphically (INTERSECTION on grapher)
Solving a 2x2 linear system algebraically by substitution method or elimination method
Special cases: no solution vs. an infinite number of solutions
Recognizing special cases algebraically and graphically
3x3 linear systems:
Solving a 3x3 linear system algebraically
Solving a 3x3 linear system electronically (using RREF)
Applications of linear systems:
2x2 mixture word problems
3x3 and higher linear system word problems
cost, revenue, profit, break-even, supply, demand, equilibrium

Objectives

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

• 5.1.1 Know all the review topics listed above
• 5.1.2 Solve 2x2 systems graphically by the intersection method
• 5.1.2 Solve 2x2 and 3x3 systems of linear equations algebraically by the substitution or elimination methods
• 5.1.4 Solve 3x3 and higher systems electronically using a simultaneous systems solver (RREF)
• 5.1.5 Solve a variety of applications of linear systems (translating the problem to a system of equations then solving electronically)

Terminology

Terms you should be able to define: system, linear equation, system of linear equations, simultaneous, 2x2 system, 3x3 system, square system, non-square system, intersection (graphical) method, substitution method, elimination method

Supplementary Resources

If you need assistance with the INTERSECTION feature of your calculator see the supplementary resources in Algebra I Lesson Notes #5.1.

For information about RREF see College Algebra Lesson Notes #5.3.

rev. 2020-11-29