Solving Systems of Linear Inequalities

Content Objectives:

Slope-intercept form of a linear equation is where m is the slope and b is the y-intercept (0,y).
The solution to a system of linear inequalities is represented by overlapping shaded areas of the system of equations.
Using the graphing method identify the solutions of a set of inequalities. If the shaded areas do not intersect there is no solution. If the shaded areas are equivalent there are infinite solutions.

Behavioral Objectives:

Write equations in slope intercept form
Graph assigned functions and identify solutions of systems of inequalities
Present findings to the class using the overhead projector and viewscreen.

Course of study and TEAM-Math objectives:

Alabama Course of Study objective 8 (Solve systems of linear equations or inequalities in two or three variables )
TEAM-Math objective A1.e (Solve equations and inequalities including linear systems in two and three variables)

Prerequisites:

Familiarity with graphing calculators, overhead projectors and viewscreens
Writing an equation in slope-intercept form

Materials:

Graphing calculator
Overhead projectors and transparencies
Viewscreen
"Solving Systems of linear inequalities" worksheet

Procedure:

LAUNCH
Instructor demonstration before the whole class
Review slope-intercept form of linear equations
Work example
Pay special attention to window settings xmin = xmin = -10 and xmax = ymax =10
Use 2nd trace = calc 5: intersection , first curve? enter, first curve? enter, Guess enter.
Use 2nd prgm = draw 7:shade, vars yvars 1:function Y1 enter , vars yvars 1:function Y2 ) enter.
The intersecting shaded area will appear.
How do you know that the shaded area is the solution to the system of inequalities?
Which inequality should be entered into Y1? Y2? Why?
Students should investigate these questions in their group work

EXPLORE
Divide the class into cooperative groups and assign each group a problem to present.
Worksheets (solutions)and calculators are distributed
Students are asked to find the solutions to the assigned problems.
Each group should prepare a transparency of their assigned problem.

SHARE/SUMMARIZE
Each group is asked to present a problem to the class
Should show how they found the solution
Should discuss any observations they made
Choose a point to verify your solution.
After all groups have finished, summarize findings.
Make sure students understand how to determine the solution to a system of equations.

Evaluation:

Walk around the room to make sure students are on the right track.
Ask questions to assure each student in the group understands key concepts.
Assure each group member has a task to complete: recorder, presenter, and question answerer.

Reference:
Molina, David d. (1995). Graphing Power, Systems of Inequalities (pp. 68-71).
Palo Alto,CA.