Chapter 5: Linear Systems Section 2: Using Algebra
Topics in Algebra 1 © 2001, 2002 Texas Instruments Teacher Notes 5-28
Linear Systems: Using Algebra Teacher Notes
Objectives
•
To review the substitution method of solving a system of two linear equations in two
variables.
•
To review the elimination method of solving a system of two linear equations in two
variables.
•
To review the definitions of consistent (independent and dependent) and inconsistent
systems.
•
To associate the number of solutions of a system with the classification of consistent
(independent and dependent) and inconsistent systems.
Math Highlights
In this section, students work with a linear system of equations with two equations and two
variables and review the methods of substitution and elimination.
In the
Overview, students associate the graphs of the lines of a system with the number of
solutions of the system and the classification of the system as consistent and inconsistent
(dependent and independent) systems. This was also covered at a lower level in
Section 1: Using Graphs & Tables.
In the substitution example, caramel corn is sold as a class fundraiser, and the students need to
know how many bags of caramel corn they need to sell to make a profit. A system of linear
equations is written to model the costs of producing the caramel corn and the revenue earned
from selling bags of caramel corn. Solving the system of equations gives the number of bags of
caramel corn the students need to sell to make a profit. The term profit is used and should be
discussed in the class. The terms breakeven and loss are not covered, but students would benefit
from a complete classroom discussion of the problem, not just the profit point.
In the elimination example, Jon and Mia earn money by recycling cans and glass. The recycling
center gives each of them one payment for both the cans and the glass. Jon and Mia want to
know how much money they earned for each pound of cans and each pound of glass. A system
of linear equations is written to model the amount of money that Jon and Mia earned for
recycling. Solving the system of equations gives the prices per pound that they were paid for
cans and glass. Students can eliminate either variable in the example.
The variables used in these problems are x and y; however, you should encourage students to
use variables that make sense in the problem.
The Try-It! examples for the TI-83 Plus and the TI-73 are slightly different. They are printed
on separate pages so that you can make copies of only the pages you need. Students can use
either calculator to complete the problems in the Student Worksheet.
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