Beginning Algebra, 11th Edition

33.Solve the system by graphing. Can you check your solution? Why or why not?

34.Explain one of the drawbacks of solving a system of equations graphically.

Without graphing, answer the following questions for each linear system. See Example 4.

(a)Is the system inconsistent, are the equations dependent, or neither?
(b)Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(c)Does the system have one solution, no solution, or an infinite number of solutions?

x- 3 y= 5

2 x+ 3 y= 6

SECTION 4.1 Solving Systems of Linear Equations by Graphing 255

30. 31. 32.

6 x- 5 = 2 y

3 x=y+ 5

4 x+ 4 = 2 y

2 x=y- 4

y=

3

2

x- 6

4 x+y= 5

35. 36. 37.

4 y=- 2 x

x+ 2 y= 0

x- 3 y=- 4

y+ 2 x= 6

x+y= 1

y-x=- 5

38. 39. 40.

2 x- y= 4

2 x+ 3 y= 12

2 x+ y= 8

x- 3 y= 5

y+ 4 = 2 x

2 x-y= 4

41. 42.

6 x+ 4 y= 3

3 x+ 2 y= 5

10 x+ 8 y= 4

5 x+ 4 y= 7

Work each problem using the graph provided.

43.The numbers of daily morning and evening news-
papers in the United States in selected years over
the period 1980–2008 are shown in the graph.
(a)For which years were there more evening
dailies than morning dailies?
(b)Estimate the year in which the number of
evening and morning dailies was closest to the
same. About how many newspapers of each
type were there in that year?
‘80 ‘85 ‘90 ‘95 ‘00 ‘05 ‘08
Year

0

200

400

600

800

1000

1400

1200

Source: Editor & Publisher

International Year Book.

Number of Newspapers

Morning Dailies

Evening Dailies

Number of Daily Newspapers

44.The graph shows how sales of music CDs and digital
downloads of single songs (in millions) in the United
States have changed over the years 2004 through 2007.
(a)In what year did Americans purchase about the
same number of CDs as single digital downloads?
How many units was this?
(b)Express the point of intersection of the two graphs as
an ordered pair of the form (year, units in millions).
(c)Describe the trend in sales of music CDs over the
years 2004 to 2007. If a straight line were used to
approximate its graph, would the line have positive,
negative, or zero slope? Explain.
(d)If a straight line were used to approximate the graph
of sales of digital downloads over the years 2004 to
2007, would the line have positive, negative, or zero
slope? Explain.

Source: Recording Industry

Association of America.

Music Going Digital

Units Sold (in millions)

CD’s

Digital

Downloads

100

200

300

400

500

700

800

900

600

’04 ’05 ’06 ’07

0

Year