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Solve the system
5x + 4y = 93x + 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) 2 • 2 + 3 • 1 ≤ 6 is false; (2, 1) is not a solution.
(b) 2 • 0 + 3 • 2 ≤ 6 is true; (0, 2) is a solution.
(c) 2 • (–4) + 3 • 2 ≤ 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 gof 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
