Beginning Algebra, 11th Edition

4.4 Applications of Linear Systems

Use the modified six-step method.

Step 1 Read.

Step 2 Assign variables.

Step 3 Write two equations using both variables.

Step 4 Solve the system.

Step 5 State the answer.

Step 6 Check.

The sum of two numbers is 30. Their difference is 6. Find the

numbers.

Let one number, and let the other number.

(1)

(2)

Add.

Divide by 2.

Let in equation (1): Solve to get

The two numbers are 18 and 12.

18 + 12 = 30 and 18 - 12 =6,so the solution checks.

x= 18 18 +y=30. y=12.

x= 18

2 x = 36

x-y= 6

x+y= 30

x= y=

4.5 Solving Systems of Linear Inequalities

To solve a system of linear inequalities, follow these steps.

Step 1 Graph each inequality on the same axes. (This
was explained in Section 3.5.)

Step 2 Choose the intersection. The solution set of the
system is formed by the overlap of the regions
of the two graphs.

The shaded region shows the solution

set of the system.

xÚ 1

2 x+ 4 yÚ 5

y

0 x

x = 1

Solution

Set

2 x + 4y = 5

REVIEW EXERCISES

CHAPTER 4

4.1 Decide whether the given ordered pair is a solution of the given system.

CONCEPTS EXAMPLES

1. 2.

2 x+ 3 y= 4

x- 4 y=- 13

1 - 5, 2 2

5 x+ y= 19

4 x- 2 y= 4

1 3, 4 2

3. 4. 5. 6.

2 x- 4 y= 4

x- 2 = 2 y

y-x=- 3

2 x+ 4 = 2 y

2 x+ y=- 2

x- 2 y= 4

2 x-y= 5

x+y= 4

Solve each system by graphing.

4.2

7.Concept Check Suppose that you were asked to solve the following system by substi-

tution. Which variable in which equation would be easiest to solve for in your first step?

5 x- 3 y= 7

• x+ 2 y= 4

288 CHAPTER 4 Systems of Linear Equations and Inequalities

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