Deck 4: Linear Systems

Question 1

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

Answer 1

4x + 3y = 36
4x + 18y = -36
-15y = 72
y = -4.8
4x + 3(-4.8) = 36
4x - 14.4 = 36
4x = 50.4
x = 12.6

Question 2

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

Answer 2

x + 7y = 0
x + 4y = 8
3y = -8
y = x + 7 = 0
x - = 0
x =

Question 3

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

Answer 3

3x + 2y = 10
2y = -3x + 10
y = + Slope, m = - , y-intercept, b = =5

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

Solve the system of equations: + = + =

Question 10

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

Question 11

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

Question 12

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

Question 13

Solve the system of equations: + = + =

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

Graph: 3x - 2y = 18

Question 22

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

Question 23

Graph: x = -4

Question 24

Graph: y = 3 - 2x

Question 25

Graph: x = 5y

Question 26

Graph: 2x - 4y = 10

Question 27

Graph: x = 7

Question 28

Graph: 5x + 4y = 20

Question 29

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

Question 30

Graph: -2y = -x + 6

Question 31

Graph: y = -4x + 16

Question 32

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

Question 33

Graph: y = -6

Question 34

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

Question 35

Graph: y = 8

Question 36

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

Question 37

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

Question 38

Graph: 7x + 4y = 0

Question 39

Graph: 3x + 4y = 12

Question 40

Graph: x + 4y = 8

Question 41

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 42

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 43

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 44

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 45

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

Question 46

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

Question 47

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 48

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

Question 49

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

Question 50

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 51

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

Question 52

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 53

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

Question 54

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 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 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 57

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

Question 58

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

Question 59

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

Question 60

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

Question 61

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 62

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 63

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

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

Question 64

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

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

Question 65

It takes your company 6 labor hours to manufacture a simple hot tub and 9 labor 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

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 67

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 68

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

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

Question 69

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 70

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

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

Question 71

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

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

Question 72

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

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

Question 73

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 74

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

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

Question 75

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

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

Question 76

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

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

Question 77

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 78

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 79

It takes a car 10 seconds to increase its speed 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 80

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

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