Alg2 3 3 systems of inequalities
- 1. Solve the system of inequalities. ALGEBRA 2 LESSON 3-3 Systems of Inequalities Graph each inequality. First graph the boundary lines. Then decide which side of each boundary line contains solutions and whether the boundary line is included. –x + y > –1 x + y > 3 –x + y > –1 x + y > 3 –x + y > –1 x + y > 3 3-3
- 2. (continued) ALGEBRA 2 LESSON 3-3 Systems of Inequalities Every point in the red region above the dashed line is a solution of –x + y > –1. Every point in the blue region above the dashed line is a solution of x + y > 3. Every point in the purple region where the red and blue regions intersect is a solution of the system. For example (2, 2) is a solution. Check: Check (2, 2) in both inequalities of the system. –x + y > –1 x + y > 3 –(2) + (2) > –1 (2) + (2) > 3 0 > –1 4 > 3 3-3
- 3. 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. ALGEBRA 2 LESSON 3-3 Systems of Inequalities 3-3 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> <
- 4. (continued) ALGEBRA 2 LESSON 3-3 Systems of Inequalities The region of overlap is a graph of the solution. Use a graphing calculator. Graph the corresponding equations m = –s + 150 and m = 60. 3-3 Since the second inequality is , shade to the right of the second line.> Since the first inequality is , shade below the first line.<
- 5. Solve the system of inequalities. ALGEBRA 2 LESSON 3-3 Systems of Inequalities y 3 y > –| x + 2| + 5 y > –| x + 2| + 5 Every point in the blue region above the dashed line is a solution of y > –| x + 2| + 5. 3-3 > y 3> y 3 y > –| x + 2| + 5 > Every point in the red region or on the solid line is a solution of y 3.>
- 6. (continued) ALGEBRA 2 LESSON 3-3 Systems of Inequalities 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. 3-3 Check: Check (4, 4) in both inequalities of the system. y 3 y > –| x + 2|+ 5 4 3 4 > –| 4 + 2|+ 5 4 > –1 >– >–
- 7. ALGEBRA 2 LESSON 3-3 Systems of Inequalities 1. Solve the system of inequalities by graphing. 2. A 24–hour radio station plays only classical music, jazz, talk programs, and news. It plays at most 12 h of music per day, of which at least 4 h is classical. Jazz gets at least 25% as much time as classical. Write and graph a system of inequalities. 3. Solve the system of inequalities by graphing. x + y 6 –x – 4y < 8 y x + 3 y |x – 2| + 1 3-3 < < > Let c = hours for classical and j = hours for jazz. c + j 12, c 4, j 0.25c< > >