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3-3 Systems of Inequalities
Solving and graphing systems of inequalities
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Objectives Solving Systems of Inequalities
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Solving a System by Using a Table
Find whole number solutions of the system using tables. x + y = 2 2x + y < 5 First make a table of values of x and y that solve the inequality.
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Continued In that table look for values of x and y that solve the
equation. Indicate any that you find. The three whole number solutions of the system are (0, 2), (1, 1), and (2, 0).
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Real World Example Jenna spends at most 150 min a night on math and science homework. She spends at least 60 min on math. Write and solve a system of inequalities to model how she allots her time for these two subjects. Relate: min on math + min on science min on math Define: Let m = the min on math. Let s = the min on science. Write: s + m , or m – s m > < The system of inequalities is m – s + 150 m 60 > <
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Continued Use a graphing calculator. Graph the corresponding
equations m = –s and m = 60. (continued) Since the first inequality is , shade below the first line. < Since the second inequality is , shade to the right of the second line. > The region of overlap is a graph of the solution.
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Solving a Linear Absolute Value System
y > –| x + 2| + 5 > Solve the system of inequalities. y 3 y > –| x + 2| + 5 > y 3 > y > –| x + 2| + 5 Every point in the red region or on the solid line is a solution of y 3. > Every point in the blue region above the dashed line is a solution of y > –| x + 2| + 5.
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Check: Check (4, 4) in both inequalities of the system.
(continued) Every point in the purple region where the red and blue regions intersect is a solution of the system. For example (4, 4) is a solution. Check: Check (4, 4) in both inequalities of the system. y y > –| x + 2|+ 5 > –| 4 + 2|+ 5 4 > –1 > –
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Homework Pg 136 # 4,7,8,18,19
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