5:40 am

Session 4 (Week 2b)

Chapter 1 Linear Equations and Inequalities

Section 1.4 Systems of Equations and Inequalities

1. Activities

W. Michael Kelley (2006). The Humongous Book of Calculus Problems.

Complete problems 1.28 - 1.33 [p. 11 - 13]

Wayne W. Dyer (2007). Change Your Thoughts - Change Your Life.

Read Verse 4: Living Infinitely [p. 19 - 23]

2. What's it all about?

This section describes two procedures (substitution and elimination) for solving a system of two equations in two unknowns.

It extends this idea to a system of inequlities, which can be represented by a region bounded by straight lines, and also provides an example of three equations with three unknowns.

3. What am I able to do, now that I am finished this section?

• solve a system of two equations in two unknowns using the elimination method
• solve a system of two equations in two unknowns using the substitution method
• solve a system of three inequalities in two unknowns and graph the result
• solve a system of three equations in three unknowns

4. What will I know?

• the logic underlying the solution to a system of equations
• the logic underlying the solution to a system of inequalities

5. What are the key concepts?

• system of equations
• system of inequalities

6. What are some relevant Web sites for this material?

Using your favorite search engine, and maybe one or two others, type in a few key words such as "two equations in two unknowns" or "system of inequalities".

Here are a few Web sites that I liked:

• http://www.webmath.com/solver2.html
• http://www.bymath.com/studyguide/alg/sec/alg15.html
• http://www.themathpage.com/alg/simultaneous-equations.htm#addition
• http://www.ucl.ac.uk/Mathematics/geomath/rev/simnb/sim3.html
• http://regentsprep.org/Regents/Math/sysineq/GrIneq.htm
• http://purplemath.com/modules/syslneq.htm

7. What concept map can I create for this section?

8. What types of Mathematica activities can I create?

Mathematica is a good software package for obtaining the graph of a specific algebraic situation.

9. What are some connections to other ideas?

This was a basic extension of the concepts of a linear equation to that of two linear equations, and then to three linear equations.

Kelley does not discuss the geometric situation corresponding to three linear equations in three unknowns. One should automatically try to visualize the geometric representation corresponding to every algebraic problem

10. What is my overall reaction to this section?

I enjoyed the problems in this section. The logic underlying the process was straight forward, the algebraic manipulations were relatively easy, and the problems easy.

11. Comments on Dyer: 4. Living Infinitely

The idea of the infinite is a commom theme in both spirituality and mathematics. One should approach mathematics with the same attitude that one does philosophy and the meaning of life. There are infinite patterns and mysteries in both. This can lead to a calm sense of insignificance as well as to awe that everything works as well as it does, in a network of inter-connectedness. Once again, this is true when considering reality and it is true when considering the inter-connections among mathematical concepts and procedures. Relax and revel in the beauty.