Use the graph shown in FIGURE 1at the beginning of this section (and repeated here) to work
Exercises 83 – 86.
83.For which years during the period 2000–2008
were sales of digital cameras less than sales of
digital camcorders?
84.Estimate the year in which sales for the two
products were the same. About what was this
sales figure?
85.If represents 2000 and represents
2008, sales in millions of units can be mod-
eled by the linear equations in the following
system.
Digital cameras
Digital camcorders
Solve this system. Express values to the nearest tenth. Write the solution as an ordered
pair of the form ( year, sales).
86.Interpret your answer for Exercise 85.How does that answer compare with your estimate
from Exercise 84?
Systems such as those in Exercises 87–90 can be solved by elimination. One way to do this is
to let and. Substitute, solve for p and q,and then find x and y. For example, in
Exercise 87, x^3 = 3 #^1 x= 3 p.BUse this method to solve each system.
q= A
1
p= y
1
x
119 x+y= 2838
624 x-y=- 1823
1 y 2
x= 0 x= 8
224 CHAPTER 4 Systems of Linear Equations
6000
8000
4000
2000
Years since 2000
Source: Consumer Electronics
Association.
0 2468
Sales
(in millions of dollars)
Digital
cameras
Smile!
Digital camcorders
87.
5
x
-
3
y
=
7
4
3
x
+
4
y
=
5
2
88.
4
x
+
1
y
=
4
5
2
x
-
5
y
=
3
2
89.
-
1
x
+
2
y
=- 1
2
x
+
3
y
=
11
2
90.
-
7
x
+
6
y
=-
3
2
4
x
-
9
y
=- 1
Brain Busters Solve by any method. Assume that a and b represent nonzero constants.
91.
ax- 2 by=c
ax+ by=c 92.
ax+ by= 2 93.
y= 5 ax
2 ax-y= 3 94.
3 ax+ 2 y= 1
Multiply both sides of each equation by the given number. See Section 2.1.
- by 4 96. by
Solve for z if and See Section 2.1.
By what number must the first equation be multiplied so that x is eliminated when the two
equations are added? See Section 4.1.
x+ 2 y+ 3 z= 9 - 3 x-y+z= 1
x= 1 y=-2.
2 x- 3 y+z= 5 - 3 x+ 8 y-z= 0 - 3
PREVIEW EXERCISES
99.
3 x- 4 y+ 2 z= 6
x+ 2 y- z= 0 100.
x- 2 y+ 5 z=- 7
