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


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
  Business and Economic applications:
  cost, revenue, profit, break-even, supply, demand, equilibrium


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


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