At the end of this lesson, students will be able to:
- Graph linear inequalities in two variables.
- Solve systems of linear inequalities.
- Solve optimization problems.
Terms introduced in this lesson:
system of inequalities
dotted line/ solid line
bounded solution/ unbounded solution
Teaching Strategies and Tips
Have students follow Example 1 step-by-step for the first few Review Questions.
- Shade each region differently.
Encourage students to rewrite each equation in slope-intercept form. This will help them graph the line and decide which half-plane to shade.
Use Example 2 as an illustration of a system of inequalities with no solution.
- Because the lines are parallel, the shaded regions will never intersect.
- It is possible, however, for lines to be parallel and have shaded regions intersect. For instance, reverse the inequalities in Example 2.
In Example 3,
- Emphasize that the method used to determine solutions to a system of inequalities can be extended to any number of inequalities.
- Point out that the pair of inequalities, and describes the first quadrant of the coordinate plane. In fact, any quadrant can be similarly described:
Quadrant I: and
Quadrant II: and
Quadrant III: and
Quadrant IV: and
Have students follow Examples 5 and 6 step-by-step for Review Question 8.
General Tip: Remind students to reverse the direction of the inequality sign when multiplying or dividing by a negative number. See Review Questions 1-7.