Lesson 6: 6-6 Systems of Inequalities
Duration of Days: 3
Lesson Objective
Solve systems of linear inequalities by graphing.
Apply systems of linear inequalities.
What kind of line represents the > symbol? What kind of line represents the = symbol?
Describe how to determine which side of the line to shade.
How can you check to make sure you shaded the correct region of the graph for the solution to a system?
System of Inequalities
A.REI.12 Graph the solutions to a linear inequalities in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in tow variables as the intersection of the corresponding half-planes.
A.CED.3 Represent constraints by equations of inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
SAT questions related to systems: 4-3-16,1-3-18,1-3-9,2-3-2,8-3-18,6-4-11,7-3-3,1-3-11,7-4-11,1-4-19,8-3-10,2-4-29,2-3-20,3-3-9
A solution of a system of inequalities is the set of all points that satisfy both inequalities. To solve the system, graph each inequality and shade the region where the graphs overlap, or intersect. If the shaded regions have no points in common, then the lines are parallel and there is no solution. If the shaded regions overlap and extend on indefinitely then there are infinitely many solutions.
A college service organization requires that its members maintain at least a 3.0 grade point average and volunteer at least 10 hours a week.
Define the variables and write a system of inequalities to represent this situation. Then graph the system.
Students may need a reminder to reverse the inequality sign if they multiply or divide by a negative number on both sides of the inequality.
If students have difficulty graphing systems of inequalities, then suggest that they graph each inequality on a separate coordinate graph and then put the tow graphs together on the same coordinate graph by copying them over or tracing them.
Extension. Have students graph 2 = x = 5 and 1 = y = 4 o the same coordinate plane. Have them describe what polygon is formed by their intersection.
Practice: Exercises #1-9
Exercises #44-48
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