Systems of Linear Equations Modeling

intro


ASL

Have you ever wondered what would be the best way to raise money for your high school prom? Are you trying to talk your parents into letting you go on a trip with your friends for spring break but money is a problem? Have you ever wondered if it was worth the time and money to start your own small business or to get a part time job? This module will help develop the skills you need in order to make these decisions.



ASL

This module uses examples of "real life" situations to teach you how to solve and graph a system of two linear equations. We will start with an example of selling donuts in order to raise money for the prom. In this example we will solve the system by graphing the two lines on the same coordinate plane. Then we will find a common point. This common point is the point where the two lines in the system meet or intersect, the "point of intersection". Then we will use the systems of equations calculator to confirm our answer.



ASL

In the next example, we will start a bumper sticker business. These equations are written in slope-intercept form. By graphing, or using the systems of equations calculator, we will find the point of intersection. At this point, we will find out how many bumper stickers we need to sell in order to break even. Then we will change one equation and find how many bumper stickers we will need to sell in order to make a $200.00 profit.



ASL

In the last example, you are going on a graduation trip. You want to rent a 15-passenger van. You will compare the prices of two companies and the distance you are traveling in order to get the best deal. You will use the systems of equations calculator to help you find the best deal.



ASL

In the second part of this module we will explore how a system of two linear equations can create two intersecting lines, two parallel lines, or one line. We will start this section with a review of section 1. You will look at the graph of three different systems and describe them. How are they the same? How are they different? Then we will look at the slopes and y-intercepts and discuss how they affect whether a system is two intersecting lines, two parallel lines, or one line. The systems of equation calculator will help you to identify these systems.



ASL

One good thing about this model is you can use the system of equations calculator for other activities at a later time.


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Developed by
The Shodor Education Foundation, Inc.

Copyright © 2002 by The Shodor Education Foundation, Inc

This project is supported, in part, by the National Science Foundation

Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.
NSF