Deck 4: Linear Systems

Question 1

Graph: x = 5y

Answer 1

Question 2

Graph: 5x + 4y = 20

Answer 2

Question 3

Graph: 7x + 4y = 0

Answer 3

Question 4

Graph: x = -4

Question 5

Graph: y = -6

Question 6

Find the slope and y-intercept: 4x + 5y = 31

Question 7

Find the slope and y-intercept: 3x + 2y = 10

Question 8

Graph: x = 7

Question 9

Find the slope and y-intercept: 4.5x + 9y = 81

Question 10

Graph: y = 3 - 2x

Question 11

Graph: 2x - 4y = 10

Question 12

Find the slope and y-intercept: 10 - y = 8x

Question 13

Graph: 3x + 4y = 12

Question 14

Find the slope and y-intercept: 2x - y = 8

Question 15

Find the slope and y-intercept: 1.5x + 3y = 2.4

Question 16

Graph: x + 4y = 8

Question 17

Find the slope and y-intercept: 1 - y = 4x

Question 18

Find the slope and y-intercept: 4 - y = 2x

Question 19

Graph: y = 8

Question 20

Find the slope and y-intercept: 3y - 5 = 2(x - 2)

Question 21

Solve graphically: 2x + 3y = -4 and x - 2y = 5

Question 22

Solve graphically: 2y = x + 200 and 3x + 2y = 240

Question 23

Solve graphically: 4x = -2y and x = 6

Question 24

The difference between seven times the first number and three times the second number is 12. The sum of three-fourths of the first number and two-thirds of the second number is 21. Find the two numbers.

Question 25

Solve graphically: 5x - 2y = 10 and y = 5

Question 26

Graph: -2y = -x + 6

Question 27

Solve graphically: x = y, 2y = x - 200

Question 28

Solve graphically: x - y = 4 and x + y = 6

Question 29

Solve graphically: 4x + 3y = 12 and 3x - 4y = -24

Question 30

Graph: y = -4x + 16

Question 31

The Oak Store has been producing 4640 chairs a day working two shifts. The second shift has produced 120 chairs fewer than four-thirds of the number of chairs produced by the first shift. Determine the number of chairs each shift has produced.

Question 32

A theatre holds 400 seats. Two types of seats are available: orchestra and balcony. The cost of an orchestra seat is $60.00 and the cost of a balcony seat is $45.00. If all 400 seats are sold the theatre would collect $22 500.00. How many of each type of seat is available?

Question 33

Twice the larger number is greater than three times the smaller number by 19. The sum of the larger number plus one-third of the smaller number is 26. Find the two numbers.

Question 34

Solve graphically: 4y = -5x and x = -6

Question 35

Solve the system graphically.

Question 36

A tavern holds 50 seats. Two types of seats are available the Friday night jazz festival: stage and dining. The cost of a stage seat is $15.00 and the cost of a dining seat is $5.00. If all 50 seats are sold the tavern would collect $400.00. How many of each type of seat is available?

Question 37

Solve graphically: y = -x - 5 and x - y = 6

Question 38

Graph: 3x - 2y = 18

Question 39

Hamidah's sales last week were $251 less than three times Colleen's sales. Together they sold $1123. Determine how much each person sold last week.

Question 40

Solve graphically: 2x = -5y and 3x + y = 9

Question 41

Find the slope of the following: 20y - 4x = 5

A) 0.8
B) 1.25
C) 0.2
D) 5
E) 4

Question 42

It takes a car 10 seconds to increase its speed from from 60 k/hr to 90 k/hr. What is the rate of acceleration (slope) in k/hr/sec?

A) 6
B) 9
C) 3
D) 1/6
E) 1/9

Question 43

A machine requires five hours to make a unit of Product A and four hours to make a unit of Product B. Last month the machine operated for 440 hours producing a total of 100 units. How many units of each type of product did it produce?

Question 44

It takes a snowboarder 46 minutes to descend from an elevation of 9200 metres to an elevation of 4508 metres. What is the rate of descent (slope) per minute?

A) 120
B) 220
C) 10.2
D) 102
E) 12.0

Question 45

A machine requires 1 hours to make a unit of Product A, and 4 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 80 units. How many hours were used to manufacture units of Product A?

Question 46

Find the slope of the line: 2y = 4(y + 2)

A) 0
B) 2
C) 4
D) 0.5
E) 1

Question 47

A machine requires 3 hours to make a unit of Product A, and 6 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 40 units. How many hours were used to manufacture units of Product A?

Question 48

Find the y-intercept for the following: 3x - 5y = 60

A) 12
B) -12
C) 60
D) -60
E) -5

Question 49

It takes your company 6 labour hours to manufacture a simple hot tub and 9 labour hours to manufacture a deluxe hot tub. Last week your company used a total of 795 labor hours to manufacture a total of 105 hot tubs. How many of each type of hot tub did you manufacture?

A) Simple 40, Deluxe 65
B) Simple 55, Deluxe 50
C) Simple 75, Deluxe 30
D) Simple 50, Deluxe 55
E) Simple 65, Deluxe 50

Question 50

Find the y-intercept for the following equation: 8x = 2 + y

A) 8
B) -8
C) 2
D) -2
E) 4

Question 51

Bonny and Clyde divide a profit of $15 700. If Clyde is to receive $4200 more than one-fifths of Bonny's share, how much will Bonny receive?

Question 52

A bakery has been baking 4000 donuts a day for distribution. . The second shift has produced 1000 donuts fewer than two-thirds of the number of donuts produced by the first shift. Determine the number of donuts each shift has produced.

Question 53

Two brothers decide to invest in a vacant lot which cost $51 000. The first brother contributes $1000 more than one-quarter of what the second brother contributes. How much does each brother contribute?

A) B1 = 11000, B2 = 40000
B) B1 = 40000, B2 = 11000
C) B1 = 12500, B2 = 38500
D) B1 = 50000, B2 = 10000
E) B1 = 1000, B2 = 50000

Question 54

Find the slope of the following: 2y - 3x = 6

A) 3
B) 1.5
C) -1.5
D) -3
E) 6

Question 55

Find the slope of the following: 2x + 5y = 50

A) 0.4
B) 2.5
C) -2.5
D) -.4
E) 10

Question 56

Find the y-intercept for the following equation: 5y + 7 = 19

A) 2.6
B) 0
C) 2.4
D) 2.8
E) 3.0

Question 57

Find the slope of the following: x + 5y = 10

A) 2
B) 0.5
C) 5
D) -0.2
E) 1

Question 58

Find the slope of the line: 2y = 5(x + 2)

A) 2
B) 5
C) 1
D) 2.5
E) 0.4

Question 59

A couple is about the get married. They decide to start a joint bank account to save for a house. They want to have an initial investment of $9000. The first partner contributes $350 more than three-quarters what the second partner contributes. How much does each partner contribute?

A) P1 = 4557.14, P2 = 4442.86
B) P1 = 3557.14, P2 = 5452.86
C) P1 = 4057.14, P2 = 4942.86
D) P1 = 5057.14, P2 = 3942.86
E) P1 = 5857.14, P2 = 3992.86

Question 60

Find the slope of the line: 4y = 5(y + 3)

A) 15
B) -15
C) 0
D) -5
E) 3

Question 61

Solve the system of equations:
3x + y = 13
x - 6y = 7

Question 62

Solve the system of equations: - = 6
3x + 4y = 12

Question 63

Solve graphically: 0.2y = 0.1x + 2 and 0.3x + 0.2y = 2.4

Question 64

An electrician charges a flat fee of $90 for a home service call. In addition he charges $25 for every 20 minutes as labour cost. If one writes an equation to calculate total charges in terms of hours of labour, what will be the slope of the line?

A) 25
B) 90
C) 50
D) 75
E) 100

Question 65

Solve the equation for x and find slope and x-intercept of 2x + 4y = 8

A) -2, 4
B) - ,2
C) -4,8
D) -2,8
E) 4,-2

Question 66

Sobeys sells fruit trays consisting of pineapple and melons. The manager of the fruit department obtains pineapples at a wholesale price of $2.50 per kg, grapes at $2.15 per kg, strawberries at $1.50 per kg and melons at $1.85 per kg. He is required to produce 10 kg of the mixed fruit. He is required to add 2 kg of strawberries and 3 kg of grapes. What is the maximum weight of pineapple that he can put in the mix in order to have an effective wholesale cost no greater than $2.00 per kg?

Question 67

Blue Mountain resort charges $39 for a single ticket for high ropes and $29 for a single ticket for low ropes. If a day's total revenue from the sale of 540 passes is $18 910, how many tickets were sold for high ropes?

Question 68

Find the slope and y-intercept: -6y - 24 = 5x

Question 69

Solve and find the value of a, given 3a + 4b = 20 and 2a + b = 15

A) a =
B) a = 7
C) a = 5
D) a = -1
E) a = 8

Question 70

Solve for x and y: 34x + 8y = 42
2y = x +

A) x = 2, y = -2
B) x = 0, y = -3
C) x = 1, y = 2
D) infinite solutions, lines coincide
E) no solutions, lines are parallel

Question 71

Graph: x =

Question 72

Operations costs increases linearly with the number of staff and are represented by the equations OC = 12000N + 3000 and 3OC - 7000N = 252000. Graphically calculate the operations cost and number of staff.

Question 73

Solve and find the value of y, given 3x + 5y = 5 and x + 2y = 1

Question 74

Solve and find the value of x, given: = and x + 5y = 38

A) x = 20
B) x = -9
C) x = 9.02
D) x = -17.16
E) x = 4.33

Question 75

How many solutions does the following system of linear equations have?
x = 3y + 4
3x - 9y = 13

Question 76

Calculate the x-intercept and y-intercept for the following equation: -x + 2y = 8

A) x-intercept does not exist; y-intercept = 4
B) -2;
C) -8; 8
D) -8; 4
E) 2;

Question 77

1000 tickets were sold for Cirque du Soleil. Adult tickets cost $8.50, children's cost $4.50, and a total of $7300 was collected. How many tickets were sold to adults?

A) 1000
B) 300
C) 700
D) 500
E) Not enough data to answer the question

Question 78

Graph: y = -

Question 79

My son and daughter were born two years apart. 9 years ago, my son was twice the age of my daughter. What are their ages now?

A) 12, 10
B) 4, 2
C) 16, 14
D) 22, 20
E) 13, 11

Question 80

The age difference between my son and me is 30 years. In 3 years from today, I will be thrice as old as my son. What is my age now?

A) 12
B) 42
C) 38
D) 45
E) 15