Intermediate Algebra (11th edition)

CHAPTER 4 Review Exercises 257

A system can be solved by matrix methods. Write the
augmented matrix and use row operations to obtain a
matrix in row echelon form.

Solve using row operations.

-^15 R 2

c

1

0

3

1

`

7

2

d

• 2R 1 +R 2

c

1

0

3

- 5

`

7

- 10

d

c

1

2

3

1

`

7

4

d

2 x+ y= 4

x+ 3 y= 7

CONCEPTS EXAMPLES

implies

y= 2

x+ 3 y= 7

When y=2,x+ 3122 =7,so x= 1 .The solution set is 51 1, 2 26.

REVIEW EXERCISES

CHAPTER 4

4.1

1.The graph shows the trends dur-

ing the years 1975 through 2007

relating to bachelor’s degrees

awarded in the United States.

(a)Between what years shown

on the horizontal axis did the

number of degrees for men

equal that for women?

(b)When the number of degrees

for men was equal to that for

women, what was that number

(approximately)?

2.Solve the system by graphing.

3.Concept Check Which ordered pair is nota solution of the equation

A. B. C. D.

4.Concept Check Suppose that two linear equations are graphed on the same set of coor-

dinate axes. Sketch what the graph might look like if the system has the given description.

(a)The system has a single solution.

(b)The system has no solution.

(c)The system has infinitely many solutions.

1 2, 0 2 1 0, 3 2 1 4, - 32 1 3, - 22

3 x+ 2 y=6?

2 x- y= 2

x+ 3 y= 8

Source: U.S. National Center for Education Statistics.

600

500

400

0

Number of Degrees

(in thousands)

1975 1980 1985 1990 1995 2000 2005

700

900

800

Bachelor's Degrees in the United States

Women

Men

Year

Write the

augmented matrix.