Section 4.5 Graphing Systems of Linear Inequalities in Two Variables

4.5 Lecture Guide: Graphing Systems of Linear Inequalities in Two Variables Objective: Graph a linear inequality in two variables.

1. Determine whether each point is a solution of (a) (b)(c) A solution of a linear inequality in two variables is an ordered pair of values that, when substituted into the inequality, makes a true statement.

Step 1. Graph the equality using (a) A _________________________ line for Graphing a Linear Inequality or (b) A _________________________ line for Step 2. Choose an arbitrary test point not on the line; is often convenient. Substitute this test point into the inequality. Step 3. (a) If the test point satisfies the inequality, shade the half-plane containing this point. (b) If the test point does not satisfy the inequality, shade the other half-plane.

Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective

3. Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective

4. Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective

5. Graph each linear inequality. Where possible, use your calculator as a check. See Calculator Perspective

Objective: Graph a system of linear inequalities. To graph a system of linear inequalities, we graph each inequality and then take as our solution the intersection of the regions shaded from each inequality.

Graph the solution of each system of linear inequalities. 6.

Graph the solution of each system of linear inequalities. 7.

Graph the solution of each system of linear inequalities. 8.

9. A local school sells student and adult tickets for basketball games. The number of student tickets x and adult tickets y sold each game are both nonnegative, and the gym holds a maximum of 2000 people. Write a system of inequalities that represents this situation and graph the solution of this system.