Chapter 3.1 Graphing Systems of Linear Inequalities

in Two Variables

Finite MathMrs. Piekos

Move from equation to inequalities◦ ax + by + c = 0 ◦ ax + by + c ≤ 0, ax + by + c ≥ 0, ax +

by + c < 0, ax + by + c > 0

Review the Shaded regions – what is or is not included with the system

Procedure for graphing inequalities Define Bounded and Unbounded Solution Sets Questions you will be asked to apply

◦ Graph the solution for the inequality◦ Write a system of linear inequalities◦ Determine the graphical solution set for each system, determine

if bounded or unbounded

Key Objectives for this unit

Graphing Linear InequalitiesEx. Graph 2 1y x

2 1y x

Notice that the line (=) is part of the solution

Also, any point in the lower half-plane satisfies the inequality so this region is shaded.

x

y

Graphing Linear Inequalities

Ex. Graph 2 1y x 2 1y x

The line (=) is not part of the solution so it is dashed.

Any point in the lower half-plane satisfies the inequality.

x

y

Procedure for Graphing Linear Inequalities

1. Draw the graph of the equation obtained by replacing the inequality symbol with an equal sign. Make the line dashed if the inequality symbol is < or >, otherwise make it solid.

2. Pick a test point in one of the half planes, substitute the x and y values into the inequality (use the origin whenever possible).

3. If the inequality is satisfied, shade the half plane containing the test point otherwise shade the other half plane.

Ex. Graph 3 2 6x y

3 2 6x y Dashed since <

True so shade region containing (0,0)

Test (0,0): 3(0)+2(0) < 6

y

x

Ex. Graph 3y 2x Ex. Graph

xx

yy

More Graphing Examples

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

1.

2.

Do Worksheet #s 1 & 2                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

                                       

Ex. Graph the solution set for the system: 2 1

3 2 6x yx y

3 2 6x y

Points must satisfy both inequalities (overlap of individual shaded regions)

2 1x y

y

x

Write a system of inequalities that describes the shaded region

Write a system of inequalities that describes the shaded region

Write a system of inequalities that describes the shaded region

3.

4.

Try these2 12

2 3 30, 0

x yx y

x y

4 5 200, 0

x yx y

Bounded Region

Unbounded Region

x

y

x

y

Regions: Bounded and Unbounded

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded

-5 5

5

-5

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded

-5 5

5

-5

Determine graphically the solution set for each system of inequalities and indicate whether the solution set is bounded or unbounded

-5 5

5

-5