3-3 Systems of Inequalities Solving and graphing systems of inequalities

Objectives Solving Systems of Inequalities

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.

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).

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 150 min on math 60 Define: Let m = the min on math. Let s = the min on science. Write:   s + m 150, or m – s + 150 m 60 > < The system of inequalities is m – s + 150 m 60 > <

Continued Use a graphing calculator. Graph the corresponding equations m = –s + 150 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.

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.

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 3 y > –| x + 2|+ 5 4 3 4 > –| 4 + 2|+ 5 4 > –1 > –

Homework Pg 136 # 4,7,8,18,19