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Section 2.2
1. Write the following system as an augmented matrix.
–5 x + 4 y  41
–3x + 5 y  35
A)  –3 –2 41


 –14 4 35
B)  –5 4 41


 –3 5 35
C)  –14 –5 41


 –10 –2 35
D) 5 –4 –41


3 –5 –35
2. Write the system corresponding to the following augmented matrix.
 5 –1 3 


 –2 5 40
A)  –3x + 15 y  3

13x – 5 y  40
B)  5 x – y  13

 –2 x + 5 y  30
C)  5 x – y  3

 –2 x + 5 y  40
D)  –3x + 13 y  3

15 x – 5 y  40
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3. Write the following system as an augmented matrix.
4 x – 3 y  –25
–2 y + 4 x  4
A)  –2 4 –25


 4 –3 4 
B)  1 –6 –25


 –3 3 4 
C)  4 –3 –25


 4 –2 4 
D)  –4 3 25 


 2 –4 –4 
4. Write the following system as an augmented matrix.
0.42 x – 0.36 y  0.084
0.05 x + 0.31y  0.62
A)  –0.42 0.36 –0.084


 –0.05 –0.31 –0.62 
B) 0.05 0.31 0.084


0.42 –0.36 0.62 
C)  1.42 0.64 0.084


 –1.95 –1.69 0.62 
D) 0.42 –0.36 0.084


0.05 0.31 0.62 
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5. Write the following system as an augmented matrix.
–0.44 x + 0.2 y  –0.212
–0.07 y + 0.46 x  1.38
A)  –0.44 0.2 –0.212


 0.46 –0.07 1.38 
B)  –0.07 0.46 –0.212


 –0.44 0.2 1.38 
C)  0.56
1.2 –0.212


 –3.07 –2.54 1.38 
D) 0.44 –0.2 0.212 


0.07 –0.46 –1.38
6. Write the following system as an augmented matrix.
–2 x – 3 y – 2 z  6
–4 x – 2 y + 2 z  2
3x + 5 y – 2 z  10
A)  –2
6
–2

 –14 –12 –7
 3
14 –2
B)  –2 –3 –2

 –14 –12 –7
 3
5
–2
C)  –2

 –4
 –6
D)  –2

 –4
 3
–3 –2
–2
2
14
7
–3 –2
–2
2
5
–2
6

6
10 
6

2
10 
6

2
10 
6

2
10 
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7. Write the system corresponding to the following augmented matrix.
 –1 2 –2 –7 


 –3 3 4 10 
 –1 –4 2 –5 
A)  – x + 2 y – 2 z  –14

 –3x + 3 y + 4 z  1
 – x – 4 y + 2z  5

B)  –8 x – 5 y – 9 z  –7

 –3x + 3 y + 4 z  10
 – x – 4 y + 2 z  –5

C)  – x + 2 y – 2 z  –7

 –12 x – 6 y + 11z  10
 – x – 4 y + 2 z  –5

D)  – x + 2 y – 2 z  –7

 –3x + 3 y + 4 z  10
 – x – 4 y + 2 z  –5

8. Write the following system as an augmented matrix.
–4 x – y + 5 z  1
y – 5x – 2 z  4
3z + 5 y + 5 x  1
A)  –4 –4 5 1 


 3 –3 1 –4 
 3 –4 5 1 
B)  –4 –1 5 1 


 3 –3 1 4 
 3 5 5 1 
C)  –4 –1 5 1 


 1 –5 –2 4 
12 –4 –4 1 
D)  –4 –1 5 1 


 –5 1 –2 4 
 5 5 3 1 
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9. Write the following system as an augmented matrix.
–0.4 x – 0.15 y + 0.26 z  –0.04
–0.15 x + 0.41y – 0.13z  0.01
0.07 x + 0.26 y + 0.05 z  –0.07
A)  –0.4 –0.14 0.26 –0.04 


 –0.05 0.51 –0.14 –0.14 
 0.07 0.29 0.05 –0.07 
B)  –0.4 –0.15 0.26 –0.04 


 –0.15 0.41 –0.13 0.01 
 0.07 0.26 0.05 –0.07 
C)  –0.4 –0.15 0.26 –0.04 


 –0.15 0.41 –0.13 0.01 
 0.04 0.29 0.08 –0.07 
D)  –0.4 –0.15 0.26 –0.04 


 –0.05 0.51 –0.14 0.01 
 0.07 0.26 0.05 –0.07 
10. Considering the following augmented matrix, perform the row operation R2  –4r1  r2 .
1 –4 –6


 4 –3 3 
A)  4 –3 –6


1 –4 3 
B) 1 –4 –6


0 13 27 
C) 6 1 –6


5 –2 3 
D)  –1 4 6 


 –4 3 –3
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11. Considering the following augmented matrix, what is the row operation that will result
in a 0 in row 2 column 1 .
1 –4 –2


3 4 –8
A) R2  0.333333r2  r1
B) R2  3r2  r1
C) R2  –3r1  r2
D) R2  –0.333333r2  r1
12. Considering the following augmented matrix:
 1 –2 –5 –3


 –2 2 4 10 
 4 4 2 –6 
Perform the row operations: R2  2r1  r2 and R3  –4r1  r3 .
A)  1 –4 –5 –3


 –8 –4 6 –4 
 4 9 2 –6 
B) 1 –2 –5 –3


0 –2 –6 4 
0 12 22 6 
C)  1 –2 –5 –3


 –2 2 4 10 
 –1 9 7 –6 
D)  1 –2 –5 –3


 –2 2 4 10 
 4 4 2 –6 
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13. Considering the following augmented matrix, what is the row operation that will result
in a 0 in row 2 column 1, and row 3 column 1
1 5 5 6 


 2 1 5 –10 
 3 –4 –5 2 
Perform the row operations: .
A) R2  2r1  r2 and R3  –3r1  r3
B) R2  –2r1  r2 and R3  3r1  r3
C) R2  0.5r1  r2 and R3  3r1  r3
D) R2  –2r1  r2 and R3  –3r1  r3
14. Write the following system as an augmented matrix.
5 x – 2 y  –9
–3 x – 2 y  –18
A)  –3 –2 –9 


 5 –2 –18
B)  5 –2 –9 


 –3 –2 –18
C)  –4 –11 –9 


 –12 –11 –18
D)  –5 2 9 


 3 2 18
15. 15 pens and 7 pencils cost a total of $7.70. 8 pens and 10 pencils cost a total of $9.15.
What linear system represents this problem?
A) 7 x + 15 y  7.70

8 x + 10 y  9.15
B) 15 x + 7 y  7.70

10 x + 8 y  9.15
C) 15 x + 7 y  7.70

8 x + 10 y  9.15
D) 7 x + 15 y  7.70

10 x + 8 y  9.15
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16. 8 pens and 7 pencils cost a total of $3.50. 6 pens and 2 pencils cost a total of $5.75.
What is the cost of each pen and pencil.
A) Pens cost $0.50 each and pencils cost $0.50 each.
B) Pens cost $1.50 each and pencils cost $0.25 each.
C) Pens cost $1.50 each and pencils cost $0.50 each.
D) Pens cost $0.50 each and pencils cost $0.25 each.
17. The local market charges $2.10 for a loaf of bread, $ 4.30 for a jar of jam, and $2.50 for
a quart of milk. One day the market sold a total of 705 loaves of bread, jars of jam, and
quarts of milk and collected a total of $2414.30. There were 3 times as many jars of
jam as loaves of bread. What linear system represents this problem?
A) 
x  y  z  705

4.3x + 2.1y + 2.5 z  2414.30

x – 3y  0

B) 
x  y  z  2.50

2.1x + 4.3 y + 2.5 z  2414.30

x – 3y  0

C) 
x  y  z  705

2.1x + 2.5 y + 4.3z  2414.30

x – 3y  0

D) 
x  y  z  705

2.1x + 4.3 y + 2.5 z  2414.30

x – 3y  0

18. The Beacon movie theater charges $7.50 for adults, $ 3.00 for children, and $1.00 for
senior citizens. One day the theater sold 463 tickets and collected $1534.00 in receipts.
There were 2 times as many children's tickets sold as adult tickets How many adults,
children, and senior citizens went to the movies that day?
A) 102 adults, 204 children, and 183 senior citizens.
B) 102 adults, 204 children, and 157 senior citizens.
C) 102 adults, 230 children, and 183 senior citizens.
D) 115 adults, 230 children, and 183 senior citizens.
19. Write the system corresponding to the following augmented matrix.
 –3 3 0 


 5 1 6
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20. Write the following system as an augmented matrix.
2 x – 2 y  –2

2 y + 2 x  –4
21. Write the following system as an augmented matrix.
 0.42 x + 0.43 y  0.085

 –0.21x + 0.04 y  –0.16
22. Write the system corresponding to the following augmented matrix.
 –1 2 4 6 


 –4 1 3 –2 
 –3 –2 –2 1 
23. Write the following system as an augmented matrix.
 –4 x + 5 y – 3z  9

 –3 y + 4 x – 3z  1
 –2 z – 3 y – x  4

24. Considering the following augmented matrix, perform the row operation R2  –2r1  r2 .
1 2 –5


 2 –1 –1
25. Considering the following augmented matrix, what is the row operation that will result
in a 0 in row 2 column 1?
1 1 4


 –3 –5 10
26. Considering the following augmented matrix:
1 4 4 –4 


5 3 4 2 
5 2 4 –6 
Perform the row operations: R2  –5r1  r2 and R3  –5r1  r3 .
60
27. 14 pens and 12 pencils cost a total of $4.25. 5 pens and 4 pencils cost a total of $12.30.
What linear system represents this problem?
28. 12 pens and 5 pencils cost a total of $5.00. 8 pens and 10 pencils cost a total of $4.50.
What is the cost of each pen and pencil?
29. The Beacon movie theater charges $15 for adults, $6 for children, and $7 for senior
citizens. One day the theater sold 28 tickets and collected $5093 in receipts. There
were 3 times as many children's tickets sold as adult tickets What linear system
represents this problem?
30. The Beacon movie theater charges $7.00 for adults, $ 4.50 for children, and $1.00 for
senior citizens. One day the theater sold 916 tickets and collected $4166.50 in receipts.
There were 3 times as many children's tickets sold as adult tickets How many adults,
children, and senior citizens went to the movies that day?
61
Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
B
C
C
D
A
D
D
C
B
B
C
B
D
B
C
D
D
B
 –3x + 3 y  0

 5x + y  6
20.  2 –2 –2


 2 2 –4
21.  0.42 0.43 0.085 


 –0.21 0.04 –0.16
22.  – x + 2 y + 4 z  6

 –4 x + y + 3z  –2
 –3x – 2 y – 2 z  1

23.  –4 5 –3 9 


 4 –3 –3 1 
 –2 –3 –1 4 
24. 1 2 –5


0 –5 9 
25. R2  3r1  r2
26. 1 4
4 –4 


0 –17 –16 22 
0 –18 –16 14 
62
27. 14 x + 12 y  4.25

 5 x + 4 y  12.30
28. Pens cost $0.25 each and pencils cost $0.30 each.
29. 
x  y  z  28

15 x + 6 y + 7 z  5093

x – 3y  0

30. 197 adults, 591 children, and 128 senior citizens.
63