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.


2 comments:

  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.

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  2. Doug,
    I'm breaking the cardinal rule of posting responses, but Nice Post. I have added the http://www.ronblond.com/M11/SYS/ 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.

    Ethan

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