Deck 8: Systems of Equations and Inequalities

Question 1

Solve the system of equations by substitution.

A)x = 0, y = 1; (0, 1)
B)x = 1, y = 0; (1, 0)
C)x = 1, y = 1; (1, 1)
D)x = 0, y = 0; (0, 0)

Answer 1

x = 0, y = 1; (0, 1)

Question 2

Solve the system of equations by substitution.

A)x = -3, y = 4; (-3, 4)
B)x = 4, y = -3; (4, -3)
C)x = -3, y = -4; (-3, -4)
D)x = -4, y = 0; (-3, 0)

Answer 2

x = -3, y = 4; (-3, 4)

Question 3

Verify that the values of the variables listed are solutions of the system of equations.
x = -1, y = 3

A)solution
B)not a solution

Answer 3

not a solution

Question 4

Solve the system of equations by substitution.

A)x = 1, y = -9; (1, -9)
B)x = -1, y = 9; (-1, 9)
C)x = 1, y = 18; (1, 18)
D)x = -1, y = -9; (-1, -9)

Question 5

Solve the system of equations by substitution.

A)x = -4, y = 0; (-4, 0)
B)x = 4, y = 0; (4, 0)
C)x = 0, y = -4; (0, -4)
D)x = 0, y = 4; (0, 4)

Question 6

Solve the system of equations by substitution.

A)x = 100, y = -27; (100, -27)
B)x = 100, y = 27; (100, 27)
C)x = -100, y = -27; (-100, -27)
D)x = -100, y = 27; (-100, 27)

Question 7

Solve the system of equations by elimination.

A)x = 15, y = -6; (15, -6)
B)x = -15, y = 5; ( -15, 5)
C)x = -15, y = 7; (-15, 7)
D)x = -6, y = 15; (-6, 15)

Question 8

Solve the system of equations by elimination.

A)x = 3, y = 8; (3, 8)
B)x = 3, y = 9; (3, 9)
C)x = 2, y = 8; (2, 8)
D)x = 2, y = 9; (2, 9)

Question 9

Solve the system of equations by substitution.

A)x = 12, y = -2; (12, -2)
B)x = -2, y = 3; (-2, 3)
C)x = 3, y = 7; (3, 7)
D)x = 7, y = 12; (7, 12)

Question 10

Verify that the values of the variables listed are solutions of the system of equations.
x = -6, y = -5

A)solution
B)not a solution

Question 11

Solve the system of equations by substitution.

A)x = 7, y = -7; (7, -7)
B)x = -7, y = 7; (-7, 7)
C)x = 6, y = -6; (6, -6)
D)x = -6, y = 6; (-6, 6)

Question 12

Verify that the values of the variables listed are solutions of the system of equations.
x = -4, y = 5

A)solution
B)not a solution

Question 13

Solve the system of equations by elimination.

A)x = 5.5, y = -8.5; (5.5, -8.5)
B)x = 5.5, y = 8.5; (5.5, 8.5)
C)x = 3, y = -8.5; (3, -8.5)
D)x = 3, y = 5.5; (3, 5.5)

Question 14

Solve the system of equations by substitution.

A)x = 3, y = 8; (3, 8)
B)x = 3, y = 9; (3, 9)
C)x = 2, y = 8; (2, 8)
D)x = 2, y = 9; (2, 9)

Question 15

Verify that the values of the variables listed are solutions of the system of equations.
x = 5, y = -1

A)solution
B)not a solution

Question 16

Solve the system of equations by substitution.

A)x = 3.5, y = -11.5; (3.5, -11.5)
B)x = 3.5, y = 11.5; (3.5, 11.5)
C)x = 8, y = -11.5; (8, -11.5)
D)x = 8, y = 3.5; (8, 3.5)

Question 17

Solve the system of equations by substitution.

A)x = 10, y = 10; (10, 10)
B)x = 0, y = 10; (0, 10)
C)x = 10, y = 0; (10, 0)
D)x = 0, y = 0; (0, 10)

Question 18

Solve the system of equations by substitution.

A)x = 5, y = -2; (5, -2)
B)x = -5, y = 2; (-5, 2)
C)x = 5, y = 2; (5, 2)
D)x = -5, y = -2; (-5, -2)

Question 19

Solve the system of equations by elimination.

A)x = 0, y = 1; (0, 1)
B)x = 1, y = 0; (1, 0)
C)x = 1, y = 1; (1, 1)
D)x = 0, y = 0; (0, 0)

Question 20

Solve the system of equations by substitution.

A)x = 5, y = -2; (5, -2)
B)x = -5, y = 2; (-5, 2)
C)x = 5, y = 2; (5, 2)
D)x = -5, y = -2; ( -5, -2)

Question 21

Solve the problem.
An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highwaydriving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?

A)153 mi
B)147 mi
C)132 mi
D)168 mi

Question 22

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 0, y = 0; (0, 0)
B)x = -9, y = -5; (-9, -5)
C)x = 0, y = -14; (0, -14)
D)inconsistent

Question 23

Write the word or phrase that best completes each statement or answers the question.
A tea shop owner is mixing a blend of two teas, one of which costs $6.50 per pound, the other costing $4.00per pound. The owner wants to have 20 pounds of a mixture that will sell for $5.50 per pound. How muchof each type of tea should be used?

Question 24

Write the word or phrase that best completes each statement or answers the question.
A store has a sale on workout gear. Mark bought three pairs of shorts and three T-shirts for $70.35 (beforetax). Later, he went back and bought two more pairs of shorts and four more T-shirts for $63.90 (beforetax). How much did the shorts and T-shirts cost?

Question 25

Solve the problem.
A tour group split into two groups when waiting in line for food at a fast food counter. The first groupbought 7 slices of pizza and 4 soft drinks for $31.35. The second group bought 5 slices of pizza and 5 softdrinks for $26.40. How much does one slice of pizza cost?

A)$3.41 per slice of pizza
B)$1.87 per slice of pizza
C)$2.91 per slice of pizza
D)$2.37 per slice of pizza

Question 26

Solve the system of equations by elimination.

A)x = 12, y = -4; (12, -4)
B)x = -12, y = 3; (-12, 3)
C)x = -12, y = 7; (-12, 7)
D)x = -4, y = 12; (-4, 12)

Question 27

Write the word or phrase that best completes each statement or answers the question.
The perimeter of a parking lot is 500 yards. Find the dimensions of the lot if the length is 50 yards morethan three times the width.

Question 28

Solve the system of equations. [Hint: Let , and solve for u and v. Then let

A)
B)
C)
D)

Question 29

Solve the system of equations by elimination.

A)x = 18,
B)x = 16,
C)x = -18,
D)x = -16,

Question 30

Solve the system of equations by elimination.

A)x = 10, y = -3; (10, -3)
B)x = -3, y = 10; (-3, 10)
C)x = -10, y = 3; (-10, 3)
D)x = 3, y = -10; (3, -10)

Question 31

Write the word or phrase that best completes each statement or answers the question.
A boat on a river goes 77 miles downstream in 2 hours and 45 minutes. The return trip takes 3 hours and30 minutes. If the boatʹs speed is the same in each direction, find the speed of the boat and the speed of thecurrent.

Question 32

Solve the problem.
A flat rectangular piece of aluminum has a perimeter of 58 inches. The length is 7 inches longer than thewidth. Find the width.

A)11 in.
B)18 in.
C)25 in.
D)29 in.

Question 33

Write the word or phrase that best completes each statement or answers the question.
Jaya has $16,000 to invest. She invests part of it in an account paying 6% simple interest and the rest in anaccount paying 7% simple interest. If her annual income is $1080, how much does she have invested ineach account?

Question 34

Solve the system of equations by elimination.

A)x = -4, y = 0; (-4, 0)
B)x = 4, y = 0; (4, 0)
C)x = 0, y = -4; (0, -4)
D)x = 0, y = 4; (0, 4)

Question 35

Solve the system of equations by elimination.

A)x = 8, y = -8; (8, -8)
B)x = -8, y = 8; (-8, 8)
C)x = 12, y = -12; (12, -12)
D)x = -2, y = 8; (-2, 8)

Question 36

Solve the problem.
The Family Fine Arts Center charges $22 per adult and $14 per senior citizen for its performances. On arecent weekend evening when 571 people paid admission, the total receipts were $9,378. How many whopaid were senior citizens?

A)398 senior citizens
B)173 senior citizens
C)308 senior citizens
D)263 senior citizens

Question 37

Solve the problem.
A movie theater charges $8.00 for adults and $5.00 for children. If there were 40 people altogether and thetheater collected $272.00 at the end of the day, how many of them were adults?

A)24 adults
B)10 adults
C)16 adults
D)29 adults

Question 38

Solve the problem.
A retired couple has $180,000 to invest to obtain annual income. They want some of it invested in safeCertificates of Deposit yielding 6%. The rest they want to invest in AA bonds yielding 11% per year. Howmuch should they invest in each to realize exactly $17,300 per year?

A)$130,000 at 11% and $50,000 at 6%
B)$130,000 at 6% and $50,000 at 11%
C)$120,000 at 6% and $60,000 at 11%
D)$140,000 at 11% and $40,000 at 6%

Question 39

Solve the problem.
The Paperback Trader is a book store that takes in used paperbacks for 20% of their cover price and sellsthem for 50% of their cover price. Pat brings in a stack of 17 paperback books to trade and gets $13.73credit. Some of the books had a cover price of $5.98, the rest $2.98. She wants to get some Tom Clancybooks having a cover price of $5.98. How many $5.98 books did she bring in and how many Clancy bookscan she get without paying any additional cash?

A)6 $5.98 books, 4 Clancy books
B)11 $5.98 books, 2 Clancy books
C)6 $5.98 books, 5 Clancy books
D)6 $5.98 books, 2 Clancy books

Question 40

Solve the system of equations by elimination.

A)x = 10, y = 10; (10, 10)
B)x = 0, y = 10; (0, 10)
C)x = 10, y = 0; (10, 0)
D)x = 0, y = 0; (0, 0)

Question 41

Solve the system of equations.

A)x = 4, y = 3, z = 5; (4, 3, 5)
B)x = 4, y = 5, z = 3; (4, 5, 3)
C)x = 5, y = 3, z = 4; (5, 3, 4)
D)inconsistent

Question 42

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 4, y = 8; (4, 8)
B)
C)x = 2, y = 3; (2, 3)
D)inconsistent

Question 43

Verify that the values of the variables listed are solutions of the system of equations.
x = 0, y = 2, z = 5

A)solution
B)not a solution

Question 44

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 4, y = 5; (4, 5)
B)
C)x = 4, y = 20; (4, 20)
D)inconsistent

Question 45

Solve the system of equations.

A)x = 1, y = -2, z = -4; (1, -2, -4)
B)x = -4, y = 1, z = -2; (-4, 1, -2)
C)x = -4, y = -2, z = 1; (-4, -2, 1)
D)inconsistent

Question 46

Solve the system of equations.

A)x = 0, y = 0, z = 1; (0, 0, 1)
B)x = 1, y = -1, z = 1; (1, -1, 1)
C)x = 0, y = 1, z = 0; (0, 1, 0)
D)x = -1, y = 1, z = 1; (-1, 1, 1)

Question 47

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A) where x is any real number or , where x is any real number}
B)x = -1,
C)x = 0, y = 12; (0, 12)
D)inconsistent

Question 48

Solve the system of equations.

A)x = 0, y = 1, z = 0; (0, 1, 0)
B)x = 0, y = 0, z = 1; (0, 0, 1)
C)x = 0, y = 1, z = -1; (0, 1, -1)
D)inconsistent

Question 49

Solve the system of equations.

A)x = 1, y = 2, z = 4; (1, 2, 4)
B)x = 1, y = 4, z = 2; (1, 4, 2)
C)x = 4, y = 2, z = 1; (4, 2, 1)
D)x = 4, y = 1, z = 2; (4, 1, 2)

Question 50

Solve the system of equations.

A)x = -2, y = -1, z = 9; (-2, -1, 9)
B)x = 2, y = -1, z = 9; (2, -1, 9)
C)x = -2, y = -1, z = -9; (-2, -1, -9)
D)x = 2, y = -1, z = -9; (2, -1, -9)

Question 51

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 2, y = 4; (2, 4)
B)x = 2, y = 3; (2, 3)
C)x = 4, y = 2; (4, 2)
D)inconsistent

Question 52

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)y = -9x + 7, where x is any real number or where x is any real number}
B)x = -9y + 7, where y is any real number or , where y is any real number}
C)y = 9x + 7, where x is any real number or , where x is any real number}
D)inconsistent

Question 53

Solve the system of equations.

A)x = -2, y = -5, z = 2; (-2, -5, 2)
B)x = -2, y = 2, z = -5; (-2, 2, -5)
C)x = 2, y = -5, z = -2; (2, -5, -2)
D)inconsistent

Question 54

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 3, y = 8; (3, 8)
B)x = 7, y = -8; (7, -8)
C)
D)inconsistent

Question 55

Verify that the values of the variables listed are solutions of the system of equations.
x = -1, y = 2, z = 4

A)solution
B)not a solution

Question 56

Solve the system of equations.

A)x = 5, y = -3, z = 1; (5, -3, 1)
B)x = 5, y = 1, z = -3; (5, 1, -3)
C)x = 1, y = -3, z = 5; (1, -3, 5)
D)inconsistent

Question 57

Solve the system of equations.

A)x = 1, y = -2, z = 4; (1, -2, 4)
B)x = 1, y = 4, z = -2; (1, 4, -2)
C)x = -2, y = 4, z = 1; (-2, 4, 1)
D)inconsistent

Question 58

Solve the system of equations.

A)x = 0, y = -5, z = -2; (0, -5, -2)
B)x = -2, y = 0, z = -5; (-2, 0, -5)
C)x = -2, y = -5, z = 0; (-2, -5, 0)
D)inconsistent

Question 59

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A) where x is any real number or where x is any real number}
B)x = 0, y = 0; (0, 0)
C)x = 6, y = 0; (6, 0)
D)inconsistent

Question 60

Solve the system of equations.

A)x = 4, y = -4, z = 1; (4, -4, 1)
B)x = 1, y = 4, z = -4; (1, 4, -4)
C)x = 1, y = -4, z = 4; (1, -4, 4)
D)inconsistent

Question 61

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
Find real numbers a, b, and c such that the graph of the function contains the points (1, 1),(2, 4), and (-3, 29).

Question 62

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 0, y = 1, z = 0; (0, 1, 0)
B)x = 4, y = 1, z = 0; (4, 1, 0)
C)x = 0, y = 0, z = 1; (0, 0, 1)
D)inconsistent

Question 63

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 64

Write the word or phrase that best completes each statement or answers the question.
Lexie wants to have an income of $9000 per year from investments. To that end she is going to invest$90,000 in three different accounts. These accounts pay 7%, 10%, and 14% simple interest. If she wants tohave $10,000 more in the account paying 7% simple interest than she has in the account paying 14% simpleinterest, how much should go into each account?

Question 65

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
Three shrimp boats supply the shrimp wholesalers on Hilton Head with fresh catch. The Annabelle takes50% of its catch to Hudsonʹs, 20% to Captain Jʹs, and 30% to Mainstreet. The Curly Q takes 40% of its catchto Hudsonʹs, 40% to Captain Jʹs, and 20% to Mainstreet. The SloJoe takes 30% of its catch to Hudsonʹs, 40%to Captain Jʹs, and 30% to Mainstreet. One week Hudsonʹs received 251.7 pounds of shrimp, Captain Jʹsreceived 217.2 pounds, and Mainstreet received 165.1 pounds. How many pounds of shrimp did each boatcatch?

A)Annabelle 182 lbs, Curly Q 251 lbs, SloJoe 201 lbs
B)Annabelle 251 lbs, Curly Q 201 lbs, SloJoe 182 lbs
C)Annabelle 201 lbs, Curly Q 251 lbs, SloJoe 182 lbs
D)Annabelle 201 lbs, Curly Q 182 lbs, SloJoe 251 lbs

Question 66

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 67

Write the augmented matrix for the system.

A)
B)
C)
D)

Question 68

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
A ceramics workshop makes wreaths, trees, and sleighs for sale at Christmas. A wreath takes 3 hours toprepare, 2 hours to paint, and 9 hours to fire. A tree takes 14 hours to prepare, 3 hours to paint, and 4hours to fire. A sleigh takes 4 hours to prepare, 16 hours to paint, and 7 hours to fire. If the workshop has113 hours for preparation time, 64 hours for painting, and 101 hours for firing, how many of each can bemade?

A)7 wreaths, 6 trees, 2 sleighs
B)6 wreaths, 2 trees, 7 sleighs
C)2 wreaths, 7 trees, 6 sleighs
D)8 wreaths, 7 trees, 3 sleighs

Question 69

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intaketo 163 g protein, 147 g fat, and 195 g carbohydrate. According to the health conscious hostess, themarinated mushroom caps have 3 g protein, 5 g fat, and 9 g carbohydrate; the spicy meatballs have 14 gprotein, 7 g fat, and 15 g carbohydrate; and the deviled eggs have 13 g protein, 15 g fat, and 6 gcarbohydrate. How many of each snack can he eat to obtain his goal?

A)9 mushrooms, 6 meatballs, 4 eggs
B)6 mushrooms, 4 meatballs, 9 eggs
C)4 mushrooms, 9 meatballs, 6 eggs
D)10 mushrooms, 7 meatballs, 5 eggs

Question 70

Write the word or phrase that best completes each statement or answers the question.
Craig, Jenni, and Jade go to a store having a sale on workout gear. Craig buys three pairs of socks, twoT-shirts, and one pair of shorts for $35.90. Jenni buys four pairs of socks, three T-shirts, and three pairs ofshorts for $71.35. Jade buys one pair of socks, four T-shirts, and 2 pairs of shorts for $59.30. What is theprice of each item?

Question 71

Solve the system of equations.

A)x = 2 - 5z, and y = 3z - 1, where z is any real number or { , and y = 3z - 1, where z is any real number}
B)x = 2 + 7z, and y = -3z - 1, where z is any real number or , and y = -3z - 1, where z is any real number}
C)x = -2 - 7z, and y = -3z -1, where z is any real number or and y = -3z -1, where z is any real number}
D)x = 1 - 5z, and where z is any real number or and , where z is any real number

Question 72

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
Find real numbers a, b, and c such that the graph of the function contains the points (1, 2),(2, 11), and (-3, -14).

Question 73

Solve the system of equations.

A)x = -3z - 5, and y = z + 2, where z is any real number or , and y = z + 2, where z is any real number}
B)x = z - 2, and y = -3z - 5, where z is any real number or { , and y = -3z - 5, where z is any real number}
C)x = 3z + 5, and y = z - 2, where z is any real number or , and y = z - 2, where z is any real number}
D)inconsistent

Question 74

Write the word or phrase that best completes each statement or answers the question.
Meisha has $25,000 that she wants to invest. She invests it in accounts paying 12%, 7%, and 6% simpleinterest. The account paying 12% is a higher-risk account, so she wants the amount in that account to behalf of the amount she has in the account paying 6% simple interest. If her annual interest is $1945, howmuch is invested at each rate?

Question 75

Write the word or phrase that best completes each statement or answers the question.
To raise money, a group of three friends is each trying to sell 100 candles. Each friend has a packagecontaining the same number of tapers, votives, and tealights. The tapers sell for $6.00 each, the votives sellfor $1.50 each, and the tealights sell for $0.75 each. Maya sold all of the candles to raise $431.25, Lorrin soldall of the tapers and tealights to raise $378.75, while Sara sold all the votives, all the tealights, and half ofthe tapers to raise $251.25. How many of each type of candle did each package contain?

Question 76

Solve the system of equations.

A)x = -3 - z, and y = 3z + 1, where z is any real number or { and y = 3z + 1, where z is any real number}
B)x = 3z + 1, and y = z - 3, where z is any real number or { and y = z - 3, where z is any real number}
C)x = z + 3, and y = 3z + 1, where z is any real number or , and y = 3z + 1, where z is any real number}
D)inconsistent

Question 77

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
The Family Arts Center charges $21 for adults, $13 for senior citizens, and $7 for children under 12 fortheir live performances on Sunday afternoon. This past Sunday, the paid revenue was $10,690 for 806tickets sold. There were 44 more children than adults. How many children attended?

A)282 children
B)238 children
C)286 children
D)272 children

Question 78

Solve the system of equations. If the system has no solution, say that it is inconsistent.

A)x = 4, y = 5, z = -2; (4, 5, -2)
B)x = -2, y = 5, z = 4; (-2, 5, 4)
C)x = -2, y = 4, z = 5; (-2, 4, 5)
D)inconsistent

Question 79

Solve the system of equations.

A)x = z + 2, and y = 2 - z, where z is any real number or , and y = 2 - z, where z is any real number}
B)x = 2 - z, and y = z + 2, where z is any real number or { , and y = z + 2, where z is any real number}
C)x = z + 2, and y = z - 2, where z is any real number or , and y = z - 2, where z is any real number}
D)inconsistent

Question 80

Write the word or phrase that best completes each statement or answers the question.
A health shop owner made trail mix containing dried fruit, nuts, and carob chips. The dried fruit sells for$5.50 per pound, the nuts sell for $7.50 per pound, and the carob chips sell for $8.50 per pound. The shopowner mixed 50 pounds of the trail mix and sells it for $6.70 per pound. If the amount of nuts is fivepounds more than the amount of carob ships, how much of each item was used for the trail mix?