Deck 4: Systems of Linear Equations

Question 1

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Answer 1

Question 2

Solve the system of linear equations by elimination.

A)
B)
C)
D) The lines coincide.
E) The lines are parallel.

Answer 2

Question 3

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Answer 3

Question 4

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 5

Solve the system of linear equations by elimination.

A)
B) The lines are parallel.
C) The lines coincide.
D)
E)

Question 6

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 7

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 8

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 9

Solve the system of linear equations by elimination.

A)
B)
C)
D) The lines are parallel.
E) The lines coincide.

Question 10

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 11

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 12

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 13

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 14

Solve the system of linear equations by elimination.

A) The lines are parallel.
B)
C)
D)
E) The lines coincide.

Question 15

Solve the system of linear equations by elimination.

A)
B) The lines are parallel.
C)
D)
E) The lines coincide.

Question 16

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 17

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 18

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 19

Solve the system of linear equations by graphing.

A)
B)
C)
D)
E)

Question 20

Jane is deciding between two sales positions. She can work for Marcy s and receive per hour or for Gigi s, where she earns per hour but also receives a commission per week. The two lines in the following figure represent the money Jane will make for working at each of the jobs. From the sketch of the graphed lines, how many hours would Jane have to work to earn the same amount at each of the positions? __________ hours If Jane expects to work less than hours a week, which job should she choose? a. Gigi s b. Marcy s __________ If Jane expects to work more than hours a week, which job should she choose? a. Gigi s b. Marcy s __________

Question 21

Multiply both sides of the bottom equation by 100 and then solve by the elimination method.

A)
B) The lines are parallel.
C)
D) The lines coincide.
E)

Question 22

Solve the system by eliminating the x variable.

Question 23

Solve the system of linear equations by elimination.

Question 24

Solve the system of linear equations by the elimination method.

A) The lines are parallel.
B)
C) The lines coincide.
D)
E)

Question 25

Solve the system of linear equations by the elimination method.

A)
B) The lines coincide.
C)
D) The lines are parallel.
E)

Question 26

Solve the system by eliminating the x variable.

A) The lines are parallel.
B)
C)
D) The lines coincide.
E)

Question 27

Solve the system by eliminating the y variable.

A) The lines coincide.
B) The lines are parallel.
C)
D)
E)

Question 28

Solve the system of linear equations by the elimination method.

A)
B) The lines are parallel.
C) The lines coincide.
D)
E)

Question 29

Solve the system of linear equations by the elimination method.

A)
B)
C) The lines coincide.
D)
E) The lines are parallel.

Question 30

Solve the system by eliminating the x variable.

A) The lines are parallel.
B)
C) The lines coincide.
D)
E)

Question 31

Solve the system by eliminating the y variable.

A)
B) The lines are parallel.
C)
D) The lines coincide.
E)

Question 32

Solve the system of linear equations by the elimination method.

A)
B) The lines are parallel.
C)
D) The lines coincide.
E)

Question 33

Solve the system of linear equations by elimination.

Question 34

Solve the system of linear equations by the elimination method.

A) The lines coincide.
B) The lines are parallel.
C)
D)
E)

Question 35

Solve the system of linear equations by the elimination method.

A) The lines are parallel.
B)
C)
D)
E) The lines coincide.

Question 36

Solve the system of linear equations by the elimination method.

A)
B)
C) The lines are parallel.
D) The lines coincide.
E)

Question 37

Solve the system by eliminating the y variable.

A) The lines coincide.
B) The lines are parallel.
C)
D)
E)

Question 38

Solve the system by eliminating the x variable.

A) The lines are parallel.
B)
C)
D) The lines coincide.
E)

Question 39

Solve the system by eliminating the y variable.

Question 40

Solve the system of linear equations by the elimination method.

Question 41

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .

A)
B)
C)
D) no solution
E) dependent

Question 42

Solve the system using the substitution method.

A) dependent
B)
C)
D) no solution
E)

Question 43

Solve the system by solving one of the equations for x or y and then use the substitution method.

A)
B) dependent
C)
D)
E) no solution

Question 44

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .

A)
B) no solution
C) dependent
D)
E)

Question 45

Solve the system by solving one of the equations for x or y and then use the substitution method.

A)
B) dependent
C)
D) no solution
E)

Question 46

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .

A)
B) no solution
C) dependent
D)
E)

Question 47

Solve the system using the substitution method.

A) dependent
B) no solution
C)
D)
E)

Question 48

Solve the system using the substitution method.

A) dependent
B)
C)
D)
E) no solution

Question 49

Solve the system using the substitution method.

A)
B)
C)
D) dependent
E) no solution

Question 50

Solve the system using the substitution method.

A)
B)
C) dependent
D) no solution
E)

Question 51

Solve the system using the substitution method.

A) no solution
B) dependent
C)
D)
E)

Question 52

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .

A)
B)
C) dependent.
D) no solution
E)

Question 53

Daniel is trying to decide whether to buy a car or a truck. The truck he is considering will cost him a month in loan payments, and it gets 15 miles per gallon in gas mileage. The car will cost a month in loan payments, but it gets miles per gallon in gas mileage. Daniel estimates that he will pay per gallon for gas. This means that the monthly cost to drive the truck x miles will be The total monthly cost to drive the car x miles will be The following figure shows the graph of each equation. At how many miles do the car and the truck cost the same to operate?

A)
B)
C)
D)
E)

Question 54

Solve the system of linear equations by the elimination method.

Question 55

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve. If the lines coincide, answer dependent . If the lines are parallel, answer no solution .

A) no solution
B)
C) dependent
D)
E)

Question 56

Solve the system using the substitution method.

A)
B) no solution
C)
D) dependent
E)

Question 57

Solve the system by solving one of the equations for x or y and then use the substitution method.

A) dependent
B)
C) no solution
D)
E)

Question 58

Solve the system by solving one of the equations for x or y and then use the substitution method.

A) dependent
B)
C) no solution
D)
E)

Question 59

Solve the system by solving one of the equations for x or y and then use the substitution method.

A) no solution
B)
C) dependent
D)
E)

Question 60

Solve the system of linear equations by the elimination method.

Question 61

How much 52% antifreeze solution and 32% antifreeze solution should be combined to give 40 gallons of 37% antifreeze solution?

A) 15 gallons at 52% solution, 25 gallons at 32% solution
B) 10 gallons at 52% solution, 30 gallons at 32% solution
C) 28 gallons at 52% solution, 12 gallons at 32% solution
D) 27 gallons at 52% solution, 13 gallons at 32% solution
E) 13 gallons at 52% solution, 27 gallons at 32% solution

Question 62

A woman invested times as much at as she did at The total amount of interest she earns in 1 year from both accounts is How much did she invest at each rate?

A)
B)
C)
D)
E)

Question 63

Solve the system by substitution. Substitute the expression in the second equation into the first equation and solve.

Question 64

The difference of two positive numbers is The larger is twice the smaller decreased by Find the two numbers.

A)
B)
C)
D)
E)

Question 65

Solve the system by solving one of the equations for x or y and then use the substitution method.

Question 66

One number is more than times another. Their sum is Find the two numbers.

A)
B)
C)
D)
E)

Question 67

The sum of two numbers is One number is times the other. Find the numbers.

A)
B)
C)
D)
E)

Question 68

A coin collector has dimes and nickels with a total face value of How many of each coin does she have?

A)
B)
C)
D)
E)

Question 69

The Bishop's Peak 4H club is having its annual fundraising dinner. Adults pay $25 apiece and children pay $10 apiece. If the number of adult tickets sold is twice the number of children's tickets sold, and the total income for the dinner is $1,800, how many of each kind of ticket did the 4H club sell?

A) 42 adults and 21 children
B) 40 adults and 20 children
C) 48 adults and 24 children
D) 60 adults and 30 children
E) 120 adults and 60 children

Question 70

Two numbers have a sum of One number is more than the other. Find the numbers.

A)
B)
C)
D)
E)

Question 71

Two positive numbers have a difference of The larger number is one more than twice the smaller. Find the two numbers.

A)
B)
C)
D)
E)

Question 72

Mr. Wilson invested money in two accounts. His total investment was If one account pays in interest and the other pays in interest, how much does he have in each account if he earned a total of in interest in 1 year?

A)
B)
C)
D)
E)

Question 73

For a Saturday matinee, adult tickets cost $6.50 and kids under 12 pay only $3.00. If 60 tickets are sold for a total of $320. How many of the tickets were adult tickets and how many were sold to kids under 12?

A) 40 adults and 20 kids
B) 50 adults and 10 kids
C) 30 adults and 30 kids
D) 45 adults and 15 kids
E) 35 adults and 25 kids

Question 74

Solve the system using the substitution method.

Question 75

A mixture of 10% disinfectant solution is to be made from 14% and 7% disinfectant solutions. How much of each solution should be used if 70 gallons of 10% solution are needed?

A) 40 gallons at 14% solution, 30 gallons at 7% solution
B) 38 gallons at 14% solution, 32 gallons at 7% solution
C) 25 gallons at 14% solution, 45 gallons at 7% solution
D) 32 gallons at 14% solution, 38 gallons at 7% solution
E) 30 gallons at 14% solution, 40 gallons at 7% solution

Question 76

Solve the system using the substitution method.

Question 77

Solve the system using the substitution method.

Question 78

Solve the system using the substitution method.

Question 79

The difference of two numbers is Their sum is Find the two numbers.

A)
B)
C)
D)
E)

Question 80

Ms. Hagan invested twice as much money in an account that pays interest as she did in an account that pays in interest. Her total investment pays her a year in interest. How much did she invest at each rate?

A)
B)
C)
D)
E)