Teacher Notes - Texas Instruments TI-83 Plus Manual Book

Chapter 5: Linear Systems
Linear Systems: Using Graphs & Tables
Objectives
•
To illustrate how to locate the real number solution of a system of linear equations (two
equations and two variables) using tables.
•
To illustrate how to locate the real number solution of a system of linear equations (two
equations and two variables) using graphs.
•
To graphically illustrate the types of solutions expected for a system of linear equations.
Math Highlights
Students work with a system of linear equations that has two equations in two variables. They
begin the Overview
can be modeled by linear equations. They investigate when the two plans cost the same amount
of money.
In the table of values example, students see a table of values for each equation. To create the
table, the equations are in the form y = mx + b. They see that the x value that gives the same y
value for both equations is the solution. They also see that they may need to refine the table of
values to search for the solution.
In the x-y graphical example, students graph both equations and locate the intersection of the
lines. The (x,y) coordinate of the intersection of the lines is the solution. Since the graphs of the
linear equations in the system can intersect, be parallel, or be the same line, students also see
that they may find a unique solution, no solution, or an infinite number of solutions to the
system.
In , students associate the graphs of the lines of a system with the number of
Observations
solutions of the system. This is covered again at a higher level in Section 2: Using Algebra.
Common Student Errors
•
Students have to rewrite the system in slope-intercept form in order to enter the equations
into the calculator. Many students tend to make sign errors and division errors when they
rewrite equations. For example, given 2T + 3S = 57 students would first have to rewrite the
equation as S = (L2/3)T + (57/3), assuming S is the dependent variable. Then, the students
have to rewrite this equation as Y1 = (L2/3)X + (57/3). A common division error is to write
the equation as Y1 = (L2/3)X + 57, which is incorrect.
•
Students forget to enter fractions into the Y= editor using parentheses. Remind students
about the order of operation. If they enter M2/3X, the calculator interprets this as L2 ÷ (3 Q X)
following the order of operation rules. The correct entry is (M2/3) Q X.
: TI-73 users can use = to enter the fractions. However, you should still remind them
Note
how to use parentheses and about the order of operation rules.
•
When solving by graphing using the graphing calculator, some students trace along one
function to what appears to be the intersection point without verifying that that point is also
on the other line.
Topics in Algebra 1
by setting up an analysis of two different cell phone plans. The two plans
© 2001, 2002 Texas Instruments
Section 1: Using Graphs & Tables

Teacher Notes

Teacher Notes 5-8