Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Systems of Linear Inequalities Solving Linear Inequalities in Two Variables Solving Systems of Linear Inequalities 4.3

When the equals sign in a linear equation in two variables is replaced with one of the symbols, or ≥, a linear inequality in two variables results. Examples: x > 4y ≥ 2x – 3 Slide 2 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Slide 3 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving linear inequalities Shade the solution set for each inequality. a.b.c. a. Begin by graphing a vertical line x = 3 with a dashed line because the equality is not included. The solution set includes all points with x-values greater than 3, so shade the region to the right of the line.

Slide 4 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving linear inequalities-continued Shade the solution set for each inequality. a.b.c. b. Begin by graphing the line y = 3x – 2 with a solid line because the equality is included. Check a test point. Try (0, 0) 0 ≤ 3(0) – 2 0 ≤ – 2 False (shade the side NOT containing (0, 0).

Slide 5 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving linear inequalities-continued Shade the solution set for each inequality. a.b.c. c. Begin by graphing the line. Use intercepts or slope- intercept form. The line is dashed. Check a test point. Try (0, 0) 0 – 3y < 6 0 – 0 < 6 0 < 6 True (shade the side containing (0, 0).

Slide 6 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Solving Systems of Linear Inequalities A system of linear inequalities results when the equals sign in a system of linear equations are replaced with, or ≥. The solution to a system of inequalities must satisfy both inequalities. Slide 7 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Slide 8 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving a system of linear inequalities Shade the solution set for each system of inequalities. a.b.c. a. Graph each line as a solid line. Shade each region. Where the regions overlap is the solution set.

Slide 9 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving a system of linear inequalities Shade the solution set for each system of inequalities. a.b.c. b. Graph each line as a solid line. Shade each region. Where the regions overlap is the solution set.

Slide 10 Copyright © 2009 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE Solution Solving a system of linear inequalities Shade the solution set for each system of inequalities. a.b.c. c. Graph each line < is dashed and ≥ is solid. Shade each region. Where the regions overlap is the solution set.