Graphing Systems of Equations

Topics for Today:

We are still working with graphing linear equations, but we've expanded our conversation to include systems of linear equations.  A linear system of equations is simply two or more linear equations containing the same variables.  When we deal in generic equations, we almost always use the variables x and y; however, when we use systems to solve real problems, we may define our variable with different letters that better match our problem.  For instance, if we are talking about costs and revenue, we may choose to use c and r for our variables.

Systems of two linear equations have three possible types of solutions because they are based upon where two lines intersect on a plane:  they either intersect nowhere, intersect at one point, or intersect at every point.  If there is a solution, it is represented as an ordered pair.

Summary of Systems of Equations
(Click Graphic to Enlarge)

Vocabulary:  system of linear equations, solution of a system of linear equations

Sections Covered in Textbook:

7-1: Solving Systems by Graphing (pages 340-345)

Resources & Tutorials:

1) What is a system of linear equations?
2) How do you solve a system using graphing?
3) What is a solution to a system of equations? 
4) What are the three types of solutions to a system of equations?

5) Solving Systems by Graphing Class Notes