Lesson 2: Modelling Linear Systems
Module 7: Systems of Linear Equations
Lesson 2 Summary
In this lesson you investigated the following questions:
- How do you decide what parts of a problem should be represented by variables?
- How do you organize the information you need to create a linear system?
In this lesson you examined situations that could be modelled by a system of linear equations. You learned how to write linear systems that can be used to solve problems. One of the initial steps in modelling situations is to define the variables or the unknown quantities. In order to know how to define the variables, you must know what type of solution the problem demands. For example, if the problem asks for the number of quarters and the number of dimes, then the variables could be defined as follows:
q = the number of quarters
d = the number of dimes
The example also shows that you can avoid confusion by defining variables using letters that have meaning in the context of the problem.
In this lesson you organized and evaluated information about given situations and then created linear systems based on your work. You used diagrams to develop meaning and to get a sense of the situation. You also used tables to sort the data. By sketching diagrams and analyzing tables, you were able to develop appropriate linear systems.
Some of the problems in this lesson were solved by graphing. Many of the other problems that you modelled in this lesson were left unsolved. In the final lesson of this module, you will revisit these problems. At that time, you will employ various strategies to determine the solutions to these problems.
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