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


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.


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


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."