Deck 5: Systems of Equations and Inequalities

Question 1

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(-4, -2) 4x + y = -14
2x + 4y = 0

A)not a solution
B)solution

Answer 1

A

Question 2

Solve the system by the addition method.

Answer 2

D

Question 3

Solve the system of equations by the substitution method.

Answer 3

C

Question 4

Solve the system of equations by the substitution method.

Question 5

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(4, 5) 4x - y = 21
3x - 4y = 32

A)solution
B)not a solution

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(-6, 2) 4x = -22 - y
2x = -4 - 4y

A)not a solution
B)solution

Question 7

Solve the system of equations by the substitution method.

Question 8

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(6, -5) 4x - y = 19
3x + 4y = -2

A)solution
B)not a solution

Question 9

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(-2, 1) 2x = 5 - y
3x = 8 - 2y

A)not a solution
B)solution

Question 10

Solve the system of equations by the substitution method.

Question 11

Solve the system of equations by the substitution method.

Question 12

Solve the system of equations by the substitution method.

Question 13

Solve the system of equations by the substitution method.

Question 14

Solve the system of equations by the substitution method.

Question 15

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(1, -4) x + y = -5
X - y = 3

A)not a solution
B)solution

Question 16

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(1, -4) x + y = -3
X - y = 5

A)solution
B)not a solution

Question 17

Choose the one alternative that best completes the statement or answers the question.
Determine whether the given ordered pair is a solution of the system
(5, 6) 4x + y = 26
2x + 4y = 34

A)not a solution
B)solution

Question 18

Solve the system of equations by the substitution method.

Question 19

Solve the system of equations by the substitution method.

Question 20

Solve the system of equations by the substitution method.

Question 21

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 22

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 23

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 24

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 25

Solve the system by the addition method.

Question 26

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 27

Solve the system by the addition method.

Question 28

Solve the system by the addition method.

Question 29

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 30

Solve the system by the addition method.

Question 31

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 32

Solve the system by the addition method.

Question 33

Solve the system by the addition method.

Question 34

Solve the system by the addition method.

Question 35

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 36

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 37

Solve the system by the addition method.

Question 38

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 39

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 40

Solve the system by the addition method.

Question 41

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

Is there a profit when 956 binoculars are produced?

A)No
B)Yes

Question 42

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 43

Solve the problem.
Two cars leave a city and head in the same direction. After 7 hours, the faster car is 42 miles ahead of the slower car. The slower car has traveled 371 miles. Find the speeds of the two cars.

A)53 mph and 59 mph
B)55 mph and 61 mph
C)47 mph and 53 mph
D)60 mph and 66 mph

Question 44

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

How many binoculars must be produced and sold for the company to break even?

A)2700 binoculars
B)750 binoculars
C)2250 binoculars
D)1500 binoculars

Question 45

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 46

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

More than how many binoculars must be produced and sold for the company to have a profit gain?

A)750 binoculars
B)2250 binoculars
C)2700 binoculars
D)1500 binoculars

Question 47

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

At the break-even point both cost and revenue are what?

A)$2250
B)$2700
C)$1500
D)$750

Question 48

Solve the problem.
An-Mei owns a business making and selling jackets. She has a fixed cost of $720. It costs $66 to produce each nd revenue function, R.

Question 49

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 50

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

Fewer than how many binoculars must be produced and sold for the company to have a profit loss?

A)2700 binoculars
B)750 binoculars
C)2250 binoculars
D)1500 binoculars

Question 51

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $117,000, plus production costs of $6000 nction, C and revenue function, R.

Question 52

Solve the problem.
The sum of two numbers is 15. If one number is subtracted from the other, their difference is 3. Find the numbers.

A)9, -6
B)-9, 6
C)13, 2
D)9, 6

Question 53

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

Question 54

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

What is the profit when 963 binoculars are produced?

A)$3426
B)$2352
C)$426
D)$5352

Question 55

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $44,000, plus production costs of $6000 per performance. A sold-out performance brings in $10,000. Determine the dollar amount coming in and going
Out at the break-even point.

A)$11
B)$66,000
C)$27,500
D)$110,000

Question 56

The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.

Is there a profit when 395 binoculars are produced?

A)No
B)Yes

Question 57

Solve the problem.
One number is 2 less than a second number. Twice the second number is 37 more than 5 times the first. Find the two numbers.

A)-11 and -9
B)9 and 11
C)-12 and -10
D)-10 and -8

Question 58

Solve the problem.
One number is 7 less than a second number. Twice the second number is 2 less than 4 times the first. Find the two numbers.

A)-15 and -8
B)8 and 15
C)7 and 14
D)9 and 16

Question 59

Solve the problem.
Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $9000 per performance. A sold-out performance brings in $15,000. Determine the number of sold-out performances,
X, needed to break even.

A)16 performances
B)5 performances
C)15 performances
D)14 performances

Question 60

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.

Question 61

Solve the problem.
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories.

Question 62

Solve the problem.
In the town of Milton Lake, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing.
Let x represent the number of years since 1990 and y represent the percentage of women in Milton Lake who
Smoke. The graph of y against x includes the data points (0, 17.5)and (14, 21.56). Let x represent the number of
Years since 1990 and y represent the percentage of men in Milton Lake who smoke. The graph of y against x
Includes the data points (0, 29.7)and (13, 27.1).
Determine when the percentage of women who smoke will be the same as the percentage of men who smoke.
Round to the nearest year. What percentage of women and what percentage of men (to the nearest whole
Percent)will smoke at that time?
[Hint: first find the slope-intercept equation of the line that models the percentage, y, of women who smoke x
Years after 1990 and the slope-intercept equation of the line that models the percentage, y, of men who smoke x
Years after 1990]

A)2019; 24%
B)2015; 25%
C)2017; 24%
D)2013; 25%

Question 63

Determine if the given ordered triple is a solution of the system.

Question 64

Solve the problem.
In Miguel's home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function y = 0.29x + 16.2 models the percentage, y, of women in this city who smoke x
Years after 1990. The function 0.21x + y = 29.0 models the percentage, y, of men in this city who smoke x years
After 1990. Use these models to determine when the percentage of women who smoke will be the same as the
Percentage of men who smoke. Round to the nearest year. What percentage of women and what percentage of
Men (to the nearest whole percent)will smoke at that time?

A)2018; 23%
B)2016; 24%
C)2015; 24%
D)2017; 23%

Question 65

Solve the problem.
In 1985, in the town of Appleby, 19.4% of Hispanics were overweight, increasing by an average of 0.41% per year. In 1985, in the town of Appleby, 0.15% of whites were overweight, increasing by an average of 32.0% per
Year. If these trends continue, in which year will the percentage of Hispanics who are overweight be the same
As the percentage of whites who are overweight? Round to the nearest year. What percentage of Hispanics (to
The nearest whole percent)will be overweight at that time?

A)1984; 19%
B)1988; 20%
C)1982; 18%
D)1986; 20%

Question 66

Solve the problem.
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers

Question 67

Solve the problem.
A rectangular lot whose perimeter is 440 feet is fenced along three sides. An expensive fencing along the lot's length costs $25 per foot , and an inexpensive fencing along the two side widths costs only $10 per foot. The
Total cost of the fencing along the three sides comes to $5150. What are the lot's dimensions?

A)Length 143 ft; Width 77 ft
B)Length 150 ft; Width 70 ft
C)Length 300 ft; Width 140 ft
D)Length 158 ft; Width 62 ft

Question 68

Solve the problem.
The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 511 people paid admission, the total receipts were $7020. How many who paid were
Senior citizens?

A)230 senior citizens
B)191 senior citizens
C)281 senior citizens
D)320 senior citizens

Question 69

Solve the problem.
Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 5 times as many dimes as nickels, and the value of the dimes is $4.50 more
Than the value of the nickels. How many nickels and dimes does Jamil have?

A)11 nickels and 55 dimes
B)10 nickels and 50 dimes
C)9 nickels and 45 dimes
D)50 nickels and 10 dimes

Question 70

Solve the problem.
As the price of a product increases, the demand for that product decreases. However, at higher prices, suppliers

Question 71

Solve the problem.
An-Mei owns a business making and selling jackets. She has a fixed cost of $1320. It costs $92 to produce each jacket. The selling price is $104 per jacket. Determine the number of jackets that must be made and sold in order
To break even.

A)112 units
B)12 units
C)111 units
D)110 units

Question 72

Solve the problem.
You invested $18,000 and started a business selling vases. Supplies cost $16 per vase and you are selling each vase for $34. Determine the number of vases, x, that must be produced and sold to break even.

A)1002 units
B)1001 units
C)1000 units
D)347 units

Question 73

Solve the problem.
In 1985, in the town of Appleby, 21.2% of Hispanics were overweight, increasing by an average of 0.41% per

Question 74

Solve the problem.
Julie and Eric row their boat (at a constant speed)45 miles downstream for 5 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 9 hours. Find the rate of the current.

A)2 mph
B)1.5 mph
C)3 mph
D)7 mph

Question 75

Solve the problem.
You invested $16,000 and started a business selling vases. Supplies cost $10 per vase and you are selling each

Question 76

Solve the problem.
A bank teller has 46 $10 and $20 bills in her cash drawer. The value of the bills is $820. How many $10 bills are there?

A)10 $10 bills
B)36 $10 bills
C)34 $10 bills
D)12 $10 bills

Question 77

Solve the problem.
Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 5 feet more than 4 times the width. He needs 70 feet of fencing to do the job. Find the length and
Width of the garden.

A)length: 57 feet; width: 13 feet
B)length: 33 feet; width: 7 feet
C)length: 25 feet; width: 5 feet
D)length: 29 feet; width: 6 feet

Question 78

Solve the problem.
A flat rectangular piece of aluminum has a perimeter of 56 inches. The length is 12 inches longer than the width. Find the width.

A)20 inches
B)32 inches
C)8 inches
D)28 inches

Question 79

Solve the problem.
A twin-engined aircraft can fly 816 miles from city A to city B in 4 hours with the wind and make the return trip in 6 hours against the wind. What is the speed of the wind?

A)34 mph
B)68 mph
C)51 mph
D)17 mph

Question 80

Solve the problem.
A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 4 bags of potato chips for $11.00. Another customer buys 3 hot dogs and 2 bags of potato chips for $7.25. Find the cost of each item.

A)$2.00 for a hot dog; $1.25 for a bag of potato chips
B)$1.00 for a hot dog; $1.75 for a bag of potato chips
C)$1.75 for a hot dog; $1.00 for a bag of potato chips
D)$1.75 for a hot dog; $1.25 for a bag of potato chips