Before attempting to complete this discussion activity, be sure you have practiced the solution techniques for systems of linear equations covered in this module.
In this discussion, you will be creating your own application problems that your fellow classmates will solve using systems of linear equations. Let's first look at an example. When creating an application problem, it is helpful to begin with the solution to the problem.
So, for example, if you start with the solutions (a rectangular garden with width = 8 ft, length = 10 ft), then you must find two ways these quantities relate to each other and give this information as clues in the problem statement. In this case, the two ways are with the perimeter = 36 ft, and the fact that the length is 2 ft longer than the width). So, your problem statement would be:
"Find the width and length of a rectangular garden if the length is two feet longer than the width and the perimeter is 36 feet."
Remember that we are dealing with systems of linear equations. That means you cannot use area or volume formulas, since those are nonlinear, meaning that they contain squared and cubed variables, respectively.
Now, let's begin our discussion of application problems involving systems of linear equations.
- Formulate two application (real-world) problems that can be solved with a system of equations in either 2 or 3 variables. Check your problem statements to make sure they include all of the information necessary to write down the governing system of equations.
- Using your problem statements, set up and solve the system of equations for each of your two problems yourself.
- Save the solutions and use them to respond to those who reply to your problems.