 # Copyright © 2011 Pearson, Inc. 7.5 Systems of Inequalities in Two Variables.

## Presentation on theme: "Copyright © 2011 Pearson, Inc. 7.5 Systems of Inequalities in Two Variables."— Presentation transcript:

Copyright © 2011 Pearson, Inc. 7.5 Systems of Inequalities in Two Variables

Copyright © 2011 Pearson, Inc. Slide 7.5 - 2 What you’ll learn about Graph of an Inequality Systems of Inequalities Linear Programming … and why Linear programming is used in business and industry to maximize profits, minimize costs, and to help management make decisions.

Copyright © 2011 Pearson, Inc. Slide 7.5 - 3 Steps for Drawing the Graph of an Inequality in Two Variables 1.Draw the graph of the equation obtained by replacing the inequality sign by an equal sign. Use a dashed line if the inequality is. Use a solid line if the inequality is ≤ or ≥. 2.Check a point in each of the two regions of the plane determined by the graph of the equation. If the point satisfies the inequality, then shade the region containing the point.

Copyright © 2011 Pearson, Inc. Slide 7.5 - 4 Example Graphing a Linear Inequality

Copyright © 2011 Pearson, Inc. Slide 7.5 - 5 Example Graphing a Linear Inequality

Copyright © 2011 Pearson, Inc. Slide 7.5 - 6 Example Solving a System of Inequalities Graphically

Copyright © 2011 Pearson, Inc. Slide 7.5 - 7 Example Solving a System of Inequalities Graphically

Copyright © 2011 Pearson, Inc. Slide 7.5 - 9 Example Solving a Linear Programming Problem

Copyright © 2011 Pearson, Inc. Slide 7.5 - 10 Example Solving a Linear Programming Problem

Copyright © 2011 Pearson, Inc. Slide 7.5 - 11 Example Solving a Linear Programming Problem

Copyright © 2011 Pearson, Inc. Slide 7.5 - 13 Quick Review Solutions

Copyright © 2011 Pearson, Inc. Slide 7.5 - 19 Chapter Test Solutions

Copyright © 2011 Pearson, Inc. Slide 7.5 - 20 Chapter Test Solutions

Copyright © 2011 Pearson, Inc. Slide 7.5 - 21 Chapter Test Solutions

Copyright © 2011 Pearson, Inc. Slide 7.5 - 22 Chapter Test Solutions

Copyright © 2011 Pearson, Inc. Slide 7.5 - 23 Chapter Test Solutions