Chapter 8 Systems Of Linear Equations And Inequalities Worksheet With Answers Page 6
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10(8–7)
399
8.1 Solving Systems by Graphing and Substitution
Solution
L
Draw a diagram as shown in Fig. 8.5. If L represents the length and W represents
W
W
the width, then we can write the following system.
L
2W
L
2L
2W
120
F I G U R E 8 . 5
Since L
2W, we can replace L in 2L
2W
120 with 2W:
2(2W)
2W
120
4W
2W
120
6W
120
W
20
I
So the width is 20 feet and the length is 2(20) or 40 feet.
E X A M P L E
8
Tale of two investments
Belinda had $20,000 to invest. She invested part of it at 10% and the remainder at
12%. If her income from the two investments was $2160, then how much did she
h e l p f u l
h i n t
invest at each rate?
In Chapter 2 we would have
Solution
done Example 8 with one
Let x be the amount invested at 10% and y be the amount invested at 12%. We can
variable by letting x represent
summarize all of the given information in a table:
the amount invested at 10%
and 20,000
x represent the
Amount
Rate
Interest
amount invested at 12%.
First investment
x
10%
0.10x
Second investment
y
12%
0.12y
We can write one equation about the amounts invested and another about the inter-
c a l c u l a t o r
est from the investments:
x
y
20,000
Total amount invested
0.10x
0.12y
2160
Total interest
c l o s e - u p
Solve the first equation for x to get x
20,000
y. Substitute 20,000
y for x in
To check Example 8, graph
the second equation:
y
20,000
x
1
0.10x
0.12y
2160
and
y
(2160
0.1x) 0.12.
0.10(20,000
y)
0.12y
2160
2
Replace x by 20,000
y.
The viewing window needs to
2000
0.10y
0.12y
2160
Solve for y.
be large enough to contain
0.02y
160
the point of intersection. Use
the intersection feature to
y
8000
find the point of intersection.
x
12,000
Because x
20,000
y
20,000
To check this answer, find 10% of $12,000 and 12% of $8000:
0.10(12,000)
1,200
0
20,000
0.12(8000)
960
Because $1200
$960
$2160 and $8000
$12,000
$20,000, we can be cer-
0
I
tain that Belinda invested $12,000 at 10% and $8000 at 12%.
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