Beginning Algebra, 11th Edition

Solving a System of Linear Inequalities

Graph the solution set of the system.

Step 1 To graph graph the solid boundary line and

shade the region containing the test point as shown in FIGURE 13(a).

Then graph with solid boundary line The

test point makes this inequality false, so shade the region on the other

side of the boundary line. See FIGURE 13(b).

1 0, 0 2

2 x- 5 yÚ 10 2 x- 5 y=10.

1 0, 0 2 ,

3 x+ 2 y...6, 3 x+ 2 y= 6

2 x- 5 yÚ 10

3 x+ 2 y... 6

EXAMPLE 1

282 CHAPTER 4 Systems of Linear Equations and Inequalities

NOW TRY
EXERCISE 1
Graph the solution set of
the system.

x+ 3 yÚ 3

4 x- 2 y... 8

x

y

0

2

3 x + 2y ≤ 6 3

(a) (b)

FIGURE 13

x

y

–2^0

3

25

3 x + 2y ≤ 6

2 x – 5y ≥ 10

Solution set

FIGURE 14

NOW TRY

x

y

0

–2

5

2 x – 5y ≥ 10

Step 2 The solution set of this system includes

all points in the intersection (overlap) of

the graphs of the two inequalities. As

shown in FIGURE 14, this intersection is

the gray shaded region and portions of

the two boundary lines that surround it.

NOW TRY ANSWER

x

y

–4

4 x – 2y ≤ 80 3

x + 3y ≥ 3

Solving a System of Linear Inequalities

Step 1 Graph the inequalities.Graph each linear inequality, using the

method described in Section 3.5.

Step 2 Choose the intersection.Indicate the solution set of the system by shad-

ing the intersection of the graphs (the region where the graphs overlap).

OBJECTIVE 1 Solve systems of linear inequalities by graphing.A system

of linear inequalitiesconsists of two or more linear inequalities. The solution set of

a system of linear inequalitiesincludes all ordered pairs that make all inequalities

of the system true at the same time.

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