Deck 5: Systems of Linear Equations and Inequalities

Question 1

Solve by substitution:

A) (0, 2)
B) Dependent,
C) (2, -8)
D) No solution
E) (1, -3)

Answer 1

Dependent,

Question 2

Solve the following system of equations by graphing:

A) No solution
B) The ordered-pair solutions of
C) (3, 2)
D) (2, 2)

Answer 2

No solution

Question 3

Solve the following system of equations by graphing:

A) (2, -1)
B) No solution
C) (0, 2)
D) (2, -1)

Answer 3

(2, -1)

Question 4

When Sara Whitehorse changed jobs, she rolled over the $54,725 in her retirement account into two simple interest accounts. On one account, the annual simple interest rate is 8.75%, and on the second account, the annual simple interest is 5%. How much must be invested in each account if the two accounts earned the same amount of annual interest?
(x at 8.75% and y at 5%.)

A) x = $19,900; y = $34,825
B) x = $19,910; y = $34,815
C) x = $34,825; y = $19,900
D) x = $20,000; y = $34,925
E) x = $20,001; y = $34,724

Question 5

Solve by the addition method:

A) (5, 7)
B) Dependent
C) No solution
D) (-1, 3)
E) (2, 5)

Question 6

Solve by substitution:

A) (4, 4)
B) (2, -1)
C) Dependent
D) No solution
E) (2, 11)

Question 7

Solve by the addition method:

A)
B)
C)
D) No solution
E)

Question 8

Solve by the addition method:

A) No solution
B) (-6,-9)
C) Dependent. The solutions satisfy .
D) (-9,-14)
E) (-3, -4)

Question 9

Solve by substitution:

A) No solution
B) (5, 4)
C) (-1, 0)
D) (2, 2)
E) Dependent

Question 10

Solve the following equations by graphing:

A) No solution
B) (3, 0)
C) (3, 2)
D) (2, 2)

Question 11

Solve by substitution:

A) (3, -2)
B) (1, 2)
C) Dependent
D) No solution
E) (2, 0)

Question 12

Solve the following system of equations by graphing:

A) (3, 2)
B) (3, 0)
C) No solution
D) The ordered-pair solutions

Question 13

An investment of $6000.00 is divided between two simple interest accounts. On one account, the annual simple interest rate is 7.75%, and on the second account, the annual simple interest is 6.25%. How much should be invested in each account so that the total interest from the two accounts is $417?
(x at 7.75% and y at 6.25%.)

A) x = $2778; y = $3222
B) x = $417; y = $5583
C) x = $2800; y = $3200
D) x = $2841; y = $3159
E) x = $3200; y = $2800

Question 14

Solve by substitution:

A) (-4, -3)
B) No solution
C) Dependent
D) (-5, -6)
E) (-6, -9)

Question 15

Solve the following equations by graphing:

A) (2, 2)
B) No solution
C) (3, 2)
D) (1, 0)

Question 16

Solve by substitution:

A) Dependent
B) No solution
C) (4, 10)
D) (5, 15)
E) (3, 5)

Question 17

Solve the following system of equations by graphing:

A) (2, 2)
B) (3, 0)
C) (1, 0)
D) No solution
E) (3, 2)

Question 18

Solve by the addition method:

A) Dependent
B) (-4, 4)
C) (2, 10)
D) No solution
E) (-1, 7)

Question 19

Is (1, -1) a solution of the following system of equations?

A) Yes
B) No

Question 20

Solve the following system of equations by graphing:

A) No solution
B) (2, -1)
C) (2, -1)
D) (0, 2)

Question 21

Graph the solution set of the following system:

A)
B)
C)
D)
E) None of the above

Question 22

Solve by the addition method:

A) (6, -1)
B) (4, -2)
C) (6, -2)
D) (5, -2)
E) (5, -1)

Question 23

A chemist has two alloys, one of which is 10% gold and 20% lead, and the other of which is 30% gold and 40% lead. How many grams of each of the two alloys should be used to make an alloy that contains 65 g of gold and 118 g of lead?

A) First alloy: 60 g; second alloy: 470 g
B) First alloy: 470 g; second alloy: 62 g
C) First alloy: 472 g; second alloy: 60 g
D) First alloy: 470 g; second alloy: 60 g
E) None of the above

Question 24

Rowing with the current, a canoeist paddled 14 mi in 2 h. Against the current, the canoeist could paddle only 6 mi in the same amount of time. Find the rate of the canoest in calm water and the rate of the current.

A) Canoeist = 6 mph; current = 3 mph
B) Canoeist = 4 mph; current = 3 mph
C) Canoeist = 7 mph; current = 4 mph
D) Canoeist = 2 mph; current = 5 mph
E) Canoeist = 5 mph; current = 2 mph

Question 25

Solve by the addition method:

A) (-3, 5)
B) (1, -1)
C) (3, -4)
D) (5, -7)
E) (-1, 2)

Question 26

An investor has a total of $24,000 deposited in three different accounts, which earn annual interest rates of 9%, 7%, and 5%. The amount deposited in the 9% account is twice the amount in the 7% account. If the three accounts earn a total annual interest of $1700, how much money is deposited in each account?

A) $10,200 at 9%; $5100 at 7%; $9000 at 5%
B) $10,000 at 9%; $5000 at 7%; $8900 at 5%
C) $10,000 at 9%; $5000 at 7%; $9000 at 5%
D) $10,200 at 9%; $5100 at 7%; $8900 at 5%
E) None of the above

Question 27

Graph the solution set of the following system:

A)
B)
C)
D)
E) None of the above

Question 28

Solve by the addition method:

A) (2, 2, 3)
B) (3, 2, 4)
C) (4, 2, 5)
D) (-3, 3, 4)
E) (3, 3, 10)

Question 29

A relief organization supplies blankets, cots, and lanterns to victims of fires, floods, and other natural disasters. One week the organization purchased 10 blankets, 10 cots, and 20 lanterns for a total cost of $1800. The second week, at the same prices, the organization purchased 20 blankets, 20 cots, and 10 lanterns for a total cost of $2400. The third week, at the same prices, the organization purchased 20 blankets, 10 cots, and 10 lanterns for a total cost of $1650. Find the cost of one blanket, the cost of one cot, and the cost of one lantern.

A) $25 per blanket; $76 per cot; $39 per lantern
B) $26 per blanket; $76 per cot; $39 per lantern
C) $25 per blanket; $75 per cot; $40 per lantern
D) $26 per blanket; $75 per cot; $40 per lantern
E) $24 per blanket; $75 per cot; $39 per lantern

Question 30

A baker purchased 14 lb of wheat flour and 16 lb of rye flour for a total cost of $21.72. A second purchase, at the same prices, included 14 lb of wheat flour and 13 lb of rye flour. The cost of the second purchase was $19.59. Find the cost per pound of the wheat flour and the rye flour.

A) Wheat: $0.64; rye: $0.71
B) Wheat: $0.74; rye: $0.66
C) Wheat: $0.74; rye: $0.71
D) Wheat: $0.71; rye: $0.74
E) Wheat: $0.76; rye: $0.71

Question 31

Graph the solution set of the following system:

A)
B)
C)
D)
E) None of the above

Question 32

A plane flying with the jet stream flew from Los Angeles to Chicago, a distance of 2568 mi, in 4 h. Flying against the jet stream, the plane could fly only 2212 mi in the same amount of time. Find the rate of the plane in calm air and the rate of the wind.

A) Plane = 577.5 mph; wind = 64.5 mph
B) Plane = 577.5 mph; wind = 24.5 mph
C) Plane = 587.5 mph; wind = 34.5 mph
D) Plane = 597.5 mph; wind = 44.5 mph
E) Plane = 607.5 mph; wind = 34.5 mph

Question 33

Solve by the addition method:

A) (3, -1, 0)
B) (3, -2, 5)
C) (8, -6, 5)
D) (4, -2, 1)
E) (2, -2, 9)

Question 34

Solve by the addition method:

A) (3, 4, 4)
B) (1, 9, 5)
C) (3, -1, 5)
D) (1, 4, 6)
E) (2, 4, 5)

Question 35

Solve by the addition method:

A) (-4, 6)
B) No solution
C) (0, 2)
D) (8, -6)
E) (4, -2)

Question 36

Graph the solution set of the following system:

A)
B)
C)
D)
E) None of the above