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: Elementary Algebra
Topic: Linear Systems
Subtopic: 3x3 Systems - Algebraically

Overview

Now that we have the basic process of algebraically solving 2x2 systems down, we are ready to extend our knowledge to 3x3 linear systems. Solving a 3x3 system algebraically still uses elimination/substitution methods, but the idea is to eliminate one variable/equation (by elmination or substitution method) to transform the 3x3 system down to a 2x2 system, solve it, then back substitute to get all three variable answers.

Objectives

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

• 5.5.1 Determine if a given ordered triple (x,y,z) is a solution to a given 3x3 system or not by algebraically "checking" it in the system's equations
• 5.5.2 Start solving a 3x3 linear systems algebraically eliminating one variable to convert it to a 2x2 linear system
• 5.5.3 After solving the "new" 2x2 linear system, use back substitution to find answer values for all three variables in the original 3x3 linear system

Terminology

Terms you should be able to define: dimension (order; size) of a system, 3x3 system (and 4x4 system, etc.), back substitution

Text Notes

When solving 3x3 and larger systems algebraically, you will only be required to solve those that have a single point answer (the consistent type). You will NOT be required to algebraically recognize the "no" solution (inconsistent) and "all" solution (dependent) types.

Geometrically it is neat to look at the 3x3 systems of intersecting planes but if you don't completely understand them, no worries, this is covered in later courses.

SKIP any "modeling" applications. This includes problems of the form, "Find the quadratic function y=ax2+bx+c whose graph passes through the given points."