Thursday, July 22, 2010

Linear Systems - Exercises vs. Problems

Linear Systems

Definition: A System of Two Linear Equations in two variables x and y, also called a linear system, consists of two equations that can be written in the following form:

Ax + By = C Equation 1
Dx + Ey = F Equation 2

A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation.

In Algebra 2, there are three different ways to solve linear systems:

  1. Solve by Graphing
  2. Solve by Substitution
  3. Solve by Elimination

Here is a link to an applet used to graph and solve linear systems: Linear Systems Applet. The screen shot is here:

Here are some textbook “recipes” for solving linear systems by two of the three methods:

The Substitution Method

The Elimination Method

Here is a problem which requires applying the knowledge learned by solving linear systems. Note that this also addresses the area of multiple representations, discussed in Week 1.


  1. Doug,
    Hope you are having fun with your youth group this week. I am learning so much with all of this nifty technology. I only hope I can remember some of it when we go back to school. Someday you'll have to explain how you imbed some of these images in your blogs. Pretty cool stuff.

  2. Doug,
    I'm breaking the cardinal rule of posting responses, but Nice Post. I have added the link to my diigo page. It will be useful for me this fall when I teach this material. The Wolfram site had the drawback that you can't play the graph after you get the answer. It's always good to discover teaching tools. Thanks.