Deck 4: Linear Systems

Question 1

Solve the system of equations: 0.8x + 0.3y = 1.3
0.3x + 0.2y = 1.1

Answer 1

Question 2

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

Answer 2

Question 3

Solve the system of equations: 5x = 10 - 2y
5y = 3x - 30

Answer 3

Question 4

Solve the system of equations: x + y = 2.5
0.2x - y = 1.2

Question 5

Solve the system of equations: 6x + 5y = 30
4x - 3y = 24

Question 6

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

Question 7

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

Question 8

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

Question 9

Solve the system of equations: 2.2x + 0.85y = 2.25
1.5x + 1.75y = 2.75

Question 10

Solve the system of equations: + = + =

Question 11

Solve the system of equations: 4x + 3y = 36
2x + 9y = -18

Question 12

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

Question 13

Solve the system of equations: + = + =

Question 14

Solve the system of equations: 4x + 18y = 36
2x + 9y = -18

Question 15

Solve the system of equations:
2x + 8y = -18
2x - 4y = 10

Question 16

Solve the system of equations: 6.6x + 3.5y = 110
2.9x + 4.7y = 106

Question 17

Solve the system of equations: 3x - 8y + 72 = 0
7x = 4y - 8

Question 18

Solve the system of equations:

Question 19

Solve the system of equations: 2x + 6y = -12
2x - 5y = 10

Question 20

Solve the system of equations: 8x + 12y = 72
6x + 7y = 84

Question 21

Graph: x + 4y = 8

Question 22

Graph: y = -4x + 16

Question 23

Graph: 3x - 2y = 18

Question 24

Graph: -2y = -x + 6

Question 25

Graph: x = 5y

Question 26

Graph: x = 7

Question 27

Graph: y = 3 - 2x

Question 28

Graph: 3x + 4y = 12

Question 29

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

Question 30

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

Question 31

Graph: y = 8

Question 32

Graph: 5x + 4y = 20

Question 33

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

Question 34

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

Question 35

Graph: 2x - 4y = 10

Question 36

Graph: y = -6

Question 37

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

Question 38

Graph: 7x + 4y = 0

Question 39

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

Question 40

Graph: x = -4

Question 41

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

Question 42

Solve the system of equations: 28 - 7x = 4y
36 - 4y = 3x

Question 43

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

Question 44

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

Question 45

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 46

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

Question 47

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 48

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

Question 49

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 50

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 51

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

Question 52

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 53

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 54

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

Question 55

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 56

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 57

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 58

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 59

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

Question 60

Solve the system graphically.
3x - 7 = y
6x -2 y = 14

Question 61

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

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

Question 62

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 63

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 64

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

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

Question 65

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 66

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 67

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 68

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 69

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

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

Question 70

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

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

Question 71

Solve for x and y: x + 9y = 18 x + 15y = 42

A)x = 18, y = 4
B)x = 18, y = -4
C)x = -18, y = -4
D)x = -18, y = 4
E)x = 4, y = -18

Question 72

Solve for the following: 2x - 3y = -24 3x + 5y = 45

A)x = 0.789, y = 8.526
B)x = .489, y = 8.526
C)x = 4.789, y = 9.526
D)x = 2.789, y = 7.526
E)x = 0.2789, y = 0.7526

Question 73

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

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

Question 74

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

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

Question 75

Solve for x and y: 4x + 9y = 72 6x + 15y = 90

A)x = 45, y = -12
B)x = -45, y = 12
C)x = 45, y = 12
D)x = -45, y = -12
E)x = -45, y = -15

Question 76

Solve for x and y: 2x + 1y = 5 4x + 2y = 20

A)x = 2, y = 1
B)x = -2, y = -1
C)x = 4, y = 2
D)x = -4, y = -2
E)no solution, the lines are parallel

Question 77

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

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

Question 78

Solve for x and y: 7x + 3y = 42 4x + 6y = 36

A)x = -4.8, y = 2.8
B)x = 4.8, y = 2.8
C)x = -4.8, y = -2.8
D)x = 4.8, y = -2.8
E)x = 4.8, y = -5.6

Question 79

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

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

Question 80

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

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