Deck 6: Systems and Matrices

Question 1

Solve the system by elimination.
7x + 9y = -7
-4x + 3y = 4

A)
B)
C)
D)

Answer 1

Question 2

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?

Answer 2

A

Question 3

Solve the system by elimination.
6x + 45= 9y
-2x - 3y=-27

A)
B)
C)
D)

Answer 3

Question 4

Solve the system by elimination.

Question 5

Solve the system by substitution.

Question 6

Solve the system by elimination.

Question 7

Solve the system by elimination.
-6x - 6y=18
2x - 4y=12

A)
B)
C)
D)

Question 8

Solve the system by substitution.

Question 9

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

Question 10

Solve the system by elimination.

Question 11

Solve the system by substitution.
-2x = 7y + 17
-31 = 3y - 3x

A)
B)
C)
D)

Question 12

Solve the system by substitution.

Question 13

Solve the system by elimination.

Question 14

Solve the system by substitution.

Question 15

Solve the system by substitution.
9x + 4y = 3
9y = 26 + 2x

A)
B)
C)
D)

Question 16

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

Question 17

Solve the system by elimination.
7x - 6y = 7
7x + 6y = 7

A)
B)
C)
D)

Question 18

Solve the system by elimination.

A)
B)
C)
D)

Question 19

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 0.92 million
C) about 0.87 million
D) about 1.03 million

Question 20

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 21

Solve the system.

A)
B)
C)
D)

Question 22

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

Question 23

Solve the system.

A)
B)
C)
D)

Question 24

Solve the system.

A)
B)
C)
D)

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 30

Solve the system.

A)
B)
C)
D)

Question 31

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

Question 32

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

Question 33

Solve the system.

A)
B)
C)
D)

Question 34

Solve the system.

A)
B)
C)
D)

Question 35

Solve the system by elimination.

A)
B)
C)
D)

Question 36

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

Question 37

Solve the system.

A)
B)
C)
D)

Question 38

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

Question 39

Solve the system.

A)
B)
C)
D)

Question 40

Solve the system.

A)
B)
C)
D)

Question 41

Solve the system.

A)
B)
C)
D)

Question 42

A) 11
B) 12
C) 10
D) 9

Question 43

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

Question 44

Find the equation of the parabola that passes through the points (-2,4),(0,-4) , and (3,2) .

A)
B)
C)
D)

Question 45

Find the equation of the circle, written in the form passing through the points (10,3),(5,-2) , and (8,7) .

A)
B)
C)
D)

Question 46

Find the equation of the line y=ax + b that passes through the points (-1,4) and (-6,-6) .

A)
B) y=2x +6
C) y=6x +2
D)

Question 47

Solve the system.

A)
B)
C)
D)

Question 48

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

Question 49

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

Question 50

Solve the system.

A)
B)
C)
D)

Question 51

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

Question 52

Solve the system in terms of the arbitrary variable x.

Question 53

Solve the system.

A)
B)
C)
D)

Question 54

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

Question 55

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

Question 56

Solve the system.

A)
B)
C)
D)

Question 57

Solve the system.

A)
B)
C)
D)

Question 58

Find the equation of the line y = ax + b that passes through the points (-3, 2) and (2, -8).

A)
B)
C) y= - 2x - 4
D) y= - 4x - 2

Question 59

Solve the system in terms of the arbitrary variable x.

Question 60

Solve the system.

A)
B)
C)
D)

Question 61

Carole's car averages 17.4 mi/gal in city driving and 25.7 mi/gal in highway driving. If she drove a total of 523.9 mi on 22 gal of gas, how many of the gallons were used for city driving?

A) 5 gal
B) 7 gal
C) 17 gal
D) 22 gal

Question 62

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 C
B) 15 A; 20 B; 15 C
C) 48 A; 20 B; 12 C
D) 20 A; 15 B; 15 C

Question 63

A) 100,100 collars
B) 49,700 collars
C) 69,700 collars
D) 64,700 collars

Question 64

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 90 red
Wires. How many of each type of cable were made?

A) 10 A; 30 B; 93 C
B) 10 A; 30 B; 20 C
C) 10 A; 103 B; 20 C
D) 20 A; 30 B; 10 C

Question 65

A $74,000 trust is to be invested in bonds paying 8%, CDs paying 5%, and mortgages paying 9%. The bond and CD investment together must equal the mortgage investment. To earn a $5930 annual income from the
Investments, how much should the bank invest in bonds?

A) $25,000
B) $37,000
C) $12,000
D) $23,000

Question 66

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

Question 67

The perimeter of a triangle is 70 cm. The triangle is isosceles now, but if its base were lengthened by 7 cm and each leg were shortened by 4 cm, it would be equilateral. Find the length of the base of the original triangle.

A) 16 cm
B) 27 cm
C) 23 cm
D) 15 cm

Question 68

The sum of a student's three scores is 223. If the first is 11 points more than the second, and the sum of the first two is 43 more than twice the third, what was the first score?

A) 60 points
B) 76 points
C) 87 points
D) 49 points

Question 69

The perimeter of a rectangle is 44 cm. The length is 12 cm longer than the width. What are the length and width of the rectangle?

A) Length: 22 cm; width: 10 cm
B) Length: 17 cm; width: 5 cm
C) Length: 23 cm; width: 11 cm
D) Length: 12 cm; width: 5 cm

Question 70

The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form that fits this data, what is the value of b ?

A) -1.2
B) -1.6
C) 1.9
D) 2.3

Question 71

Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1500 gal of gasohol containing 10% alcohol?

A) 429 gal 5%; 1071 gal 12%
B) 625 gal 5%; 875 gal 12%
C) 75 gal 5%; 180 gal 12%
D) 1071 gal 5%; 1071 gal 12%

Question 72

A grain dealer sold to one customer 2 bushels of wheat, 9 of corn, and 6 of rye for $45.20; to another, 9 of wheat, 6 of corn, and 2 of rye for $35.60; and to a third, 6 of wheat, 2 of corn, and 9 of rye for $45.00. What was the price
Per bushel for corn?

A) $2.10
B) $3.40
C) $2.40
D) $1.60

Question 73

Bob fenced in a rectangular garden in his yard. The length of the rectangle is 5 ft longer than the width and the perimeter is 66 ft. What is the width of the rectangle?

A) 28 ft
B) 13 ft
C) 16 ft
D) 14 ft

Question 74

A) 80.1 lb
B) 82.8 lb
C) 83.9 lb
D) 82.4 lb

Question 75

Michael's bank contains only nickels, dimes, and quarters. There are 67 coins in all, valued at $5.25. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters. How many dimes are in
The bank?

A) 7 dimes
B) 10 dimes
C) 50 dimes
D) 15 dimes

Question 76

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 6% cement should he mix with 3 bags of 12% cement to produce a mix containing 7% cement?

A) 23 bags
B) 17 bags
C) 18 bags
D) 15 bags

Question 77

The perimeter of a rectangle is 64 m. If the width were doubled and the length were increased by 5 m, the perimeter would be 100 m. What are the length and width of the rectangle?

A) Length: 16 m; width: 11 m
B) Length: 13 m; width: 19 m
C) Length: 16 m; width: 16 m
D) Length: 19 m; width: 13 m

Question 78

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 79

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 $163 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile?

A) $17 per day; 13¢ per mile
B) $13 per day; 17¢ per mile
C) $16 per day; 14¢ per mile
D) $18 per day; 14¢ per mile

Question 80

The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form that fits this data, what is the value of c?

A) 23.6
B) 14
C) 20
D) 12.8