Warm up Solve the system 5x + 4y = 9 3x + y = 11 WorldCom charges $179 for installation of a TV system and $17.50 per month. Satellite, Inc. Charges $135 for installation and $21.50 per month. Which system should Maria decide to use?

Systems of Linear Inequalities © 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 2 8.2

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 3 Solve Linear Inequalities Examples:

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 4 Example: Which of the following ordered pairs are solutions of the inequality (a) (2, 1) (b) (0, 2) (c) (–4, 2) Solve Linear Inequalities

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 5 Example: Which of the following ordered pairs are solutions of the inequality (a) (2, 1) (b) (0, 2) (c) (–4, 2) Solution: (a) ≤ 6 is false; (2, 1) is not a solution. (b) ≤ 6 is true; (0, 2) is a solution. (c) 2 (–4) ≤ 6 is true; (–4, 2) is a solution. Solve Linear Inequalities

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 6 Example: Solve the inequality Solution: We can rephrase the inequality as the pair of statements Solve Linear Inequalities (continued on next slide)

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 7 Solve Linear Inequalities Points on or above the line are solutions. Points below the line are not.

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 8 Solve Linear Inequalities 1)Graph the equation just like y = mx + b 2)Check whether the line is solid or dotted 3)Test a point to determine where to shade

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 9 Example: Solve the inequality Solve Linear Inequalities (continued on next slide)

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 10 Example: Solve the inequality Solution: Step 1: Graph as a solid line. Step 2: Test the point (0, 0) to see that 4(0) – 3(0) ≥ 9 is not true. We conclude that the (0, 0) side of the line does not contain solutions to the inequality. Solve Linear Inequalities (continued on next slide)

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 11 Solve Linear Inequalities

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 12 Solving Systems of Linear Inequalities (continued on next slide) Example: Solve the system

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 13 Solving Systems of Linear Inequalities (continued on next slide) Example: Solve the system Solution: Graph using a dotted line and graph using a solid line. Testing (0, 0) in the inequalities, is not a solution to the first inequality but is a solution to the second inequality.

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 14 Solving Systems of Linear Inequalities The point (3, 4) is called a corner point.

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 15 Modeling with Systems of Inequalities (continued on next slide) Example: A serving of fried shrimp contains approximately 15 g of protein and 60 mg of calcium. A spear of broccoli contains 5 g of protein and 80 mg of calcium. Assume that, in his diet, a man wants to get at least 60 g of protein and 600 mg of calcium from fried shrimp and broccoli. Express this pair of conditions as a system of inequalities and graph its solution set.

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 16 (continued on next slide) Solution: Assume the man eats s servings of shrimp and b spears of broccoli. Modeling with Systems of Inequalities

© 2010 Pearson Education, Inc. All rights reserved.Section 8.2, Slide 17 We obtain the system whose solution is below. Modeling with Systems of Inequalities