Chapter+03+Notes

Now we will move on to Chapter 3: Solving Systems of Equations. These lessone will build on the ideas of the previous chapter and use the ideas of quick graphical constructions as we learn how to find when different linear models are equal to one another.

In this chapter we will also begin using technology much more often. In class we will have access to the TI-83Plus calculators. These tools are great for streamlining the process of graphing. They will not be used for everything. Students will be expected to show their work and thought processes whether they use the calculators or do all of the work by hand. Included herein is a link to a PDF file of the manual for these calculators. You can find others in the Download section of TI's website at education.ti.com.

In this section we are introduced to systems of equations. The systems are defined and we learn of the three types of solution sets that we can have with linear models. This section also teachs us how to solve these systems by graphing.

In this section we move on to the types of systems that do not work out so nicely and where graphing is not an option. We learn how to use different types of substitutions to change the equations so that they are for only one variable and solve them down from there.

Our second algebraic way of solving systems of equations is through a process called elimination. This adds the equations in special ways so that one variable disappears. Also included with this lesson is how to expand these ideas for a larger system of equations such as 3 equations for three unknowns.

Taking what we had from last chapter and applying it to systems of equations we now are working with systems of inequalities. These can only be readily solved through graphing. Instead of a single point we are looking for a field or region of the plane.

With this lesson we begin a look at linear programming. It is a method for finding minimum and maximum values for a set of limitations called constraints. We graph the constraints, find the vertices of their common region and test them in another function called the Objective. This is a type of 3-D graphing in a 2-D system.

Part 2 of this section deals with the application of Linear Programming. These notes walk us through one example form the textbook. Also included is a set of directions for using the TI-83 to compute the objective function. These directions can also be found in the textbook immediately following section 3.4.

Extension: In order to have one extra item to practice all of these ideas together with I have added one more linear programming problem to do. Enjoy the Shopping Spree.

As a quick review before the test that is coming, here are some exercises that are similar to what we will see on the test. Enjoy!