August 11, 2007
This session is based on the material in section 1.4 of Kelley's "The Humongous Book of Calculus Problems"
The section presents a series of problems involving the solution to two equations in two unknowns, three equations in three unknowns, and a system of inequalities. I am going to use Mathematica to obtain the graphical representation corresponding to some of these problems.

This is usually a two-step process. First one needs to input the expression into Mathematica. Then one needs to input the appropriate expression to obtain the graph.

Here is the first problem, # 1.28 One is supposed to solve a given system of two equations.

Obtaining the solution using Mathematica is easy. But there is little underlying understanding of what is happening. Let's now see the graphical situation.

Two questions occur to me. One: can I create a pinwheel using a large number of lines that all pass through one point? Two: can I create a pinwheel that is centered about an arbitrary point? I will come back to this later.
Here are a few additional parameters that are useful when plotting functions:
AspectRatio -> 1, Automatic (equal scale for both axes)
PlotRange -> Automatic is equivalent to {{xmin, xmax}, Automatic}

Let's try to graph a system of inequalities.

Created by Mathematica  (August 17, 2007)