Deck 9: Systems and Matrices

Question 1

Solve the system by substitution.

Answer 1

C

Question 2

Solve the system by elimination.

Answer 2

C

Question 3

Solve the system by substitution.

Answer 3

A

Question 4

Solve the system by substitution.

Question 5

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.
Express the solution of the system as an ordered pair.

A) approximately (3.9, 0.92)
B) approximately (1.2, 1.03)
C) approximately (4.6, 0.87)
D) approximately (3.1, 0.95)

Question 6

Solve the system by substitution.

Question 7

Solve the system by substitution.

Question 8

Solve the system by substitution.

Question 9

Solve the system by elimination.

Question 10

Solve the system by elimination.

Question 11

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.
If equations of the form y = f(t) were determined that modeled either of the two graphs, then the variable t would represent and the variable y would represent .

A) population (in millions); year
B) City Y; City X
C) City X; City Y
D) year; population (in millions)

Question 12

Solve the system by elimination.

Question 13

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.
In what years was the population of the City X metropolitan area less than that of the City Y metropolitan area?

A) Years 1-5
B) Years 3-5
C) Years 5-6
D) Years 1-3

Question 14

Solve the system by elimination.

Question 15

Solve the system by elimination.

Question 16

Solve the system by substitution.

Question 17

Solve the system by elimination.

Question 18

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.
Use the terms increasing, decreasing, and/or constant to describe the trends for the population of the City X metropolitan area.

A) The population of the City X metropolitan area was increasing from Year 1 to Year 6.
B) The population of the City X metropolitan area was decreasing from Year 1 to Year 5 and was constant from Year 5 to Year 6.
C) The population of the City X metropolitan area was decreasing from Year 1 to Year 6.
D) The population of the City X metropolitan area was increasing from Year 1 to Year 5 and was constant from Year 5 to Year 6.

Question 19

Solve the system by elimination.

Question 20

The following graph shows the populations of the metropolitan areas of City X and City Y over six years.
At the time when the populations of the two metropolitan areas were equal, what was the approximate population of each area?

A) about 0.95 million
B) about 0.87 million
C) about 0.92 million
D) about 1.03 million

Question 21

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

Question 22

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

Question 23

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

Question 24

Solve the system.

Question 25

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 26

Solve the system.

Question 27

Solve the system.

Question 28

Solve the system.

Question 29

Solve the system.

Question 30

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

Question 31

Solve the system.

Question 32

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 33

Solve the system.

Question 34

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 35

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 36

Solve the system.

Question 37

Use a graphing calculator to solve the system. Express solutions with approximations to the nearest thousandth.

Question 38

Solve the system by elimination.

Question 39

Solve the system.

Question 40

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 41

Solve the system.

Question 42

Solve the system.

Question 43

Solve the problem.

Question 44

Solve the system in terms of the arbitrary variable x.

Question 45

Solve the problem.

Question 46

Solve the system.

Question 47

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 48

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 49

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 50

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 51

Solve the system in terms of the arbitrary variable x.

Question 52

Solve the system.

Question 53

Solve the system.

Question 54

Solve the system.

Question 55

Solve the problem.

Question 56

Solve the problem.

Question 57

Solve the problem.

Question 58

Solve the system.

Question 59

Solve the system.

Question 60

Solve the system. If the system has infinitely many solutions, write the solution set with x arbitrary.

Question 61

Solve the problem.
A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 95 black, 100
White and 80 red wires. How many of each type of cable were made?

A) 15 A; 16 B; 15 CB)15 A; 20 B; 15 CC)48A; 20 B; 12 CD)20 A; 15 B; 15 C

Question 62

Solve the problem.

Question 63

Solve the problem.
A grain dealer sold to one customer 10 bushels of wheat, 8 of corn, and 5 of rye for $67.80; to another, 8 of wheat, 5 of corn, and 10 of rye for $67.90; and to a third, 5 of wheat, 10 of corn, and 8
Of rye for $69.00. What was the price per bushel for corn?

A) $3.30
B) $3.10
C) $2.80
D) $3.00

Question 64

Solve the problem.
A $64,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $4910
Annual income from the investments, how much should the bank invest in bonds?

A) $21,000
B) $32,000
C) $11,000
D) $9,000

Question 65

Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 5% cement should he mix with 14 bags of 14.5% cement to produce a mix containing 12% cement?

A) 24 bags
B) 5 bags
C) 19 bags
D) 7 bags

Question 66

Solve the problem.
Bob fenced in a rectangular garden in his yard. The length of the rectangle is 7 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

A) 15 ft
B) 26 ft
C) 13 ft
D) 12 ft

Question 67

Solve the problem.
The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 10 m, the perimeter would be 70 m. What are the length and width of the rectangle?

A) Length: 9 m; width: 4 m
B) Length: 13 m; width: 6 m
C) Length: 6 m; width: 13 m
D) Length: 9 m; width: 9 m

Question 68

Solve the problem.
The sum of a studentʹs three scores is 218. If the first is 10 points more than the second, and the sum of the first two is 20 more than twice the third, what was the first score?

A) 56 points
B) 66 points
C) 81 points
D) 71 points

Question 69

Solve the problem.
The perimeter of a triangle is 81 cm. The triangle is isosceles now, but if its base were lengthened by 4 cm and each leg were shortened by 5 cm, it would be equilateral. Find the length of the base
Of the original triangle.

A) 25 cm
B) 20 cm
C) 21 cm
D) 30 cm

Question 70

Solve the problem.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $90 for 3 days and 300 miles, while Mary was charged $162 for 5 days and 600 miles. What does Best Rental
Charge per day and per mile?

A) $17 per day; 13¢ per mile
B) $19 per day; 13¢ per mile
C) $12 per day; 18¢ per mile
D) $18 per day; 12¢ per mile

Question 71

Solve the problem.

Question 72

Solve the problem.
Michaelʹs bank contains only nickels, dimes, and quarters. There are 65 coins in all, valued at $5.30. The number of nickels is 3 short of being three times the sum of the number of dimes and quarters.
How many dimes are in the bank?

A) 8 dimes
B) 9 dimes
C) 48 dimes
D) 14 dimes

Question 73

Solve the problem.
Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is 1500 L/hr. What is the flow in each pipe?

A) 600 L/hr hot; 900 L/hr cold
B) 500 L/hr hot; 750 L/hr cold
C) 900 L/hr hot; 600 L/hr cold
D) 750 L/hr hot; 500 L/hr cold

Question 74

Solve the problem.
The perimeter of a rectangle is 50 cm. The length is 11 cm longer than the width. What are the length and width of the rectangle?

A) Length: 11 cm; width: 7 cm
B) Length: 25 cm; width: 14 cm
C) Length: 18 cm; width: 7 cm
D) Length: 21 cm; width: 10 cm

Question 75

Solve the problem.
Caroleʹs car averages 12.9 mi/gal in city driving and 21.8 mi/gal in highway driving. If she drove a total of 320.3 mi on 20 gal of gas, how many of the gallons were used for city driving?

A) 15 gal
B) 12 gal
C) 13 gal
D) 7 gal

Question 76

Solve the problem.
Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1000 gal of gasohol containing 10% alcohol?

A) 714 gal 5%; 714 gal 12%
B) 417 gal 5%; 583 gal 12%
C) 50 gal 5%; 120 gal 12%
D) 286 gal 5%; 714 gal 12%

Question 77

Solve the problem.
Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The combined income from the 5% and 6%
Investments is the same as the income from the 8% investment. Find the amount invested at each
Rate.

A) $8000 at 5%; $10,000 at 6%; $7000 at 8%
B) $10,000 at 5%; $5000 at 6%; $10,000 at 8%
C) $10,000 at 5%; $10,000 at 6%; $5000 at 8%
D) $5000 at 5%; $10,000 at 6%; $10,000 at 8%

Question 78

Solve the problem.
A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110
White and 80 red wires. How many of each type of cable were made?

A) 20 A; 20 B; 83 CB)20 A; 93 B; 10 CC)10A; 20 B; 20 CD)20 A; 20 B; 10 C

Question 79

Solve the problem.

Question 80

Solve the problem.