Deck 8: Systems of Equations

Question 1

Solve graphically.

A)Infinite number of solutions
B)(5, -2)
C)No solution
D)(0, 18)

Answer 1

A

Question 2

Solve and graph.
x + y = -14 2x - 2y = -14

A)Inconsistent and independent
B)Consistent and dependent
C)Inconsistent and dependent
D)Consistent and independent

Answer 2

D

Question 3

Classify the system as consistent or inconsistent, and dependent or independent.
x + y = 11 y = 2x + 5

A)(3, 8)
B)(2, 9)
C)(9, 2)
D)(1, 11)

Answer 3

B

Question 4

Classify the system as consistent or inconsistent, and dependent or independent.
x - 3y = 6 3y + 1 = x

A)Inconsistent and independent
B)Consistent and dependent
C)Inconsistent and dependent
D)Consistent and independent

Question 5

Solve graphically.

A)No solution
B)(1, 5)
C)Infinite number of solutions
D)(1, 1)

Question 6

Solve and graph.
4x - 5y = -4 16x - 20y = -16

A)Inconsistent and independent
B)Consistent and dependent
C)Consistent and independent
D)Inconsistent and dependent

Question 7

Solve graphically.
3x + y = -6 2x + 4y = 6

A)(-3, 3)
B)(-1, -3)
C)(-3, -4)
D)(3, 3)

Question 8

Solve and graph.
4x + 2y = 8 2x - y = 4

A)Inconsistent and dependent
B)Consistent and independent
C)Consistent and dependent
D)Inconsistent and independent

Question 9

Solve graphically.

A)(-1.5, -1)
B)(1.5, -1)
C)No solution
D)(1, 1)

Question 10

Solve and graph.
x + 4y = 22 2x + 8y = 44

A)Inconsistent and dependent
B)Consistent and independent
C)Consistent and dependent
D)Inconsistent and independent

Question 11

Solve and graph.
3x = y + 3 6x - 2y = 3

A)Inconsistent and dependent
B)Consistent and dependent
C)Inconsistent and independent
D)Consistent and independent

Question 12

Classify the system as consistent or inconsistent, and dependent or independent.
y = 3x + 4 2x + y = 19

A)(13, -7)
B)(13, 3)
C)(3, 13)
D)(2, 10)

Question 13

Solve graphically.

A)(2, 1)
B)(1, 2)
C)No solution
D)Infinite number of solutions

Question 14

Solve and graph.

A)Infinitely many solutions
B)No solution
C)(5, 3)
D)(3, 5)

Question 15

Solve graphically.

A)(3, 4)
B)(3, 1)
C)(4, 3)
D)(4, -3)

Question 16

Solve graphically.
-2x + 4y = 2 3x + 4y = 27

A)No solution
B)(5, 3)
C)(3, 5)
D)(-2, 33)

Question 17

Solve and graph.
x - 6 = y y + 9 = x

A)Inconsistent and dependent
B)Inconsistent and independent
C)Consistent and dependent
D)Consistent and independent

Question 18

Solve and graph.
x + y = 0 x - y = 18

A)Inconsistent and dependent
B)Inconsistent and independent
C)Consistent and independent
D)Consistent and dependent

Question 19

Solve and graph.
5x - 25y = 20

A)Consistent and independent
B)Consistent and dependent
C)Inconsistent and independent
D)Inconsistent and dependent

Question 20

Solve and graph.
x + 5y = 12 3x - 4y = -2

A)Consistent and independent
B)Consistent and dependent
C)Inconsistent and dependent
D)Inconsistent and independent

Question 21

Solve using the substitution method.
x + 2y = -3 8x + 3y = -24

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

Question 22

Solve using the substitution method.
x + 7y = 47 8x + 6y = 26

A)(-3, 8)
B)(-2, 7)
C)(2, 8)
D)No solution

Question 23

Solve by the substitution method.
- x + 4y = + 2 -3x - 4y = -26

A)(-2, 6)
B)No solution
C)(7, 1)
D)(6, 2)

Question 24

Solve by the substitution method.
The perimeter of a triangle is 52 cm. The triangle is isosceles now, but if its base were lengthened by 3 cm and each leg were shortened by 2 cm, it would be equilateral. Find the base of the original triangle.

A)17 cm
B)13 cm
C)19 cm
D)14 cm

Question 25

Solve the problem.
The perimeter of a rectangle is 54 m. If the width were doubled and the length were increased by 15 m, the perimeter would be 98 m. What are the length and width of the rectangle?

A)width 8 m, length 13 m
B)width 7 m, length 20 m
C)width 13 m, length 13 m
D)width 20 m, length 7 m

Question 26

Solve the problem.
The sum of two numbers is 39 and their difference is 17. Find the numbers.

A)13 and 30
B)26 and 13
C)28 and 11
D)23 and 16

Question 27

Solve using the substitution method.
x + y = -2 x + y = -7

A)No solution
B)(0, -9)
C)(0, 0)
D)(-2, -7)

Question 28

Solve by the substitution method.
2 x - y = 9 5x + y = 33

A)(3, 6)
B)(6, 4)
C)(6, 3)
D)No solution

Question 29

Solve the problem.
The sum of two angles is 211°. One angle is 29° less than twice the other. Find the angles.

A)127° and 84°
B)78° and 127°
C)80° and 131°
D)78° and 133°

Question 30

Solve using the substitution method.
x + y = 6 5x + 5y = 30

A)(0, 0)
B)(6, 5)
C)Infinite number of solutions
D)(3, 3)

Question 31

Solve the problem.
Two angles have a sum of 96°. Their difference is 22°. Find the angles.

A)39° and 61°
B)75° and 21°
C)57° and 39°
D)59° and 37°

Question 32

Solve using the substitution method.
7x + 6y = 55 -5x - 4y = -39

A)(6, 2)
B)(7, 1)
C)(7, 2)
D)No solution

Question 33

Solve using the substitution method.
x - 4y = 20 4x - 3y = 15

A)(1, -6)
B)(5, 0)
C)(0, -5)
D)No solution

Question 34

Solve using the substitution method.
7x - 5y = 20 -3x + 3y = -12

A)(0, -4)
B)(0, -3)
C)(-1, -3)
D)No solution

Question 35

Solve using the substitution method.
6x + 30 = 6y 3x - 4y = -16

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

Question 36

Solve using the substitution method.
x = 4 + -4y x + 4y = 7

A)Infinitely many solutions
B)No solution
C)(- 1, 8)
D)(- 1, - 8)

Question 37

Solve the problem.
Find two numbers whose sum is 35 and whose difference is 5.

A)31 and 4
B)15 and 20
C)22 and 27
D)13 and 22

Question 38

Solve the problem.
The perimeter of a rectangle is 44 cm. One side is 10 cm longer than the other side. Find the lengths of the sides.

A)6 cm, 10 cm
B)12 cm, 22 cm
C)9 cm, 19 cm
D)6 cm, 16 cm

Question 39

Solve using the substitution method.
-7x + 8y = 42 2x + 6y = -12

A)(-6, 1)
B)No solution
C)(-6, 0)
D)(-7, 1)

Question 40

Solve by the substitution method.
x + y = -13 x - y = -1

A)(-7, -6)
B)(-8, -5)
C)No solution
D)(7, -5)

Question 41

Solve using the elimination method.
x + 8y = 8 6x + 9y = 48

A)(8, 0)
B)(-8, -1)
C)no solution
D)(9, 8)

Question 42

Solve using the elimination method.

Question 43

Solve using the elimination method.
-4x + 4y = 6 12x - 12y = 18

A)(-24, 24)
B)infinitely many solutions
C)no solution
D)(24, -24)

Question 44

Solve the problem using the elimination method.
Two angles are supplementary, and one is 5° more than six times the other. Find the larger angle.

A)155°
B)25°
C)70°
D)110°

Question 45

Solve using the elimination method.
0.8x + 0.3y = 10.7 -0.3x - 0.1y = -3.9

A)(100, 90)
B)(1, 0.9)
C)(10, 9)
D)(9, 10)

Question 46

Solve using the elimination method.
9x + 7y = 49 -3x - 5y = -35

A)(0, 8)
B)no solution
C)(0, 7)
D)(-1, 8)

Question 47

Solve the problem using the elimination method.
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $81 for 3 days and 300 miles, while Mary was charged $144 for 5 days and 600 miles. What does Best Rental charge per day and
Per mile?

Question 48

Solve the problem using the elimination method.
There were 380 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $600. How many adults and how many children attended?

A)150 adults and 230 children
B)80 adults and 300 children
C)160 adults and 220 children
D)220 adults and 160 children

Question 49

Solve using the elimination method.
-7x + 9y = 28 -3x - 3y = 12

A)no solution
B)(-4, 1)
C)(-5, 1)
D)(-4, 0)

Question 50

Solve using the elimination method.
x + 3y = 13 2x + 3y = 8

A)No solution
B)(5, 5)
C)(-4, -5)
D)(-5, 6)

Question 51

Solve using the elimination method.
x - 2y = 8 -7x - 3y = -39

A)(6, -1)
B)no solution
C)(5, 0)
D)(-6, 0)

Question 52

Solve the problem using the elimination method.
There were 31,000 people at a ball game in Los Angeles. The day's receipts were $180,000. How many people paid $11 for reserved seats and how many paid $4 for general admission?

A)23,000 paid $11 and 8000 paid $4
B)17,000 paid $11 and 14,000 paid $4
C)8000 paid $11 and 23,000 paid $4
D)14,000 paid $11 and 17,000 paid $4

Question 53

Solve using the elimination method.
x + 5y = 25 2x + 6y = 30

A)(-5, 0)
B)no solution
C)(0, 5)
D)(1, 4)

Question 54

Solve the problem using the elimination method.
In a right triangle, one acute angle is 54° more than twice the other. Find each acute angle.

A)28° and 62°
B)37° and 53°
C)21° and 69°
D)12° and 78°

Question 55

Solve using the elimination method.

Question 56

Solve the problem using the elimination method.
Two angles are supplementary, and one is 40° more than three times the other. Find the smaller angle.

A)35°
B)145°
C)105°
D)75°

Question 57

Solve using the elimination method.
2.5x + 0.2y = 10.6 0.5x - 0.4y = 0.8

A)(4.5, 3)
B)(6.5, 3.2)
C)(4, 3)
D)(1.5, 3.2)

Question 58

Solve using the elimination method.
0.1x + 0.7y = 1.7 x - 0.3y = -4.9

A)(-4, 3)
B)(3, -4)
C)(-0.4, 0.3)
D)no solution

Question 59

Solve the problem using the elimination method.
A salesman sold $300 more than the rest of the sales staff. If the sales total for the day was $1050, how much did the rest of the sales staff sell?

A)$375
B)$675
C)$750
D)$525

Question 60

Solve using the elimination method.
-3x - 2y = 4 12x + 8y = -16

A)(-12, -8)
B)infinitely many solutions
C)(-8, -12)
D)no solution

Question 61

Solve the problem.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 6% and the rest at 8%. He made a total of $480 in interest. How much was invested at 8%?

A)$5000
B)$3500
C)$4000
D)$3000

Question 62

Solve the problem.
Ellen wishes to mix candy worth $1.57 per pound with candy worth $3.69 per pound to form 26 pounds of a mixture worth $3.04 per pound. How many pounds of the more expensive candy should she use?

A)8 pounds
B)18 pounds
C)23 pounds
D)10 pounds

Question 63

Solve the problem.
A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 3% cement should he mix with 8 bags of 11% cement to produce a mix containing 7% cement?

A)21 bags
B)16 bags
C)8 bags
D)10 bags

Question 64

Solve the problem.
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 19 pounds of feed worth $0.76 per pound by mixing one kind worth $0.41 per pound with another worth $0.96 per pound. How many pounds of
The cheaper kind should they use in the mix?

A)17 pounds
B)12 pounds
C)7 pounds
D)9 pounds

Question 65

Solve the problem using the elimination method.
A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.50. Another customer buys 5 hot dogs and 3 bags of potato chips for $14.25. Find the cost of each item.

A)$2.25 for a hot dog; $1.00 for a bag of potato chips
B)$2.50 for a hot dog; $1.25 for a bag of potato chips
C)$1.00 for a hot dog; $2.25 for a bag of potato chips
D)$2.25 for a hot dog; $1.25 for a bag of potato chips

Question 66

Solve the problem.
Anne and Nancy use a metal alloy that is 17% copper to make jewelry. How many ounces of an alloy that is 11% copper must be mixed with an alloy that is 22% copper to form 55 ounces of the desired alloy?

A)35 ounces
B)27 ounces
C)30 ounces
D)25 ounces

Question 67

Solve the problem using the elimination method.
The sum of two numbers is 8. Three times the larger number plus four times the smaller number is 18. Find the numbers.

A)6 and 2
B)6 and -14
C)14 and -6
D)22 and -14

Question 68

Solve the problem.
A sum of money amounting to $4.15 consists of dimes and quarters. If there are 28 coins in all, how many are quarters?

A)21 quarters
B)14 quarters
C)9 quarters
D)19 quarters

Question 69

Solve the problem.
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 30 coins with a total face value of $4.90, how many of the coins are nickels?

A)22 nickels
B)13 nickels
C)17 nickels
D)15 nickels

Question 70

Solve the problem.
How many liters of a 10% alcohol solution must be mixed with 90 liters of a 70% solution to get a 60% solution?

A)108 L
B)1.8 L
C)18 L
D)10.8 L

Question 71

Solve the problem.
There were 520 people at a play. The admission price was $3 for adults and $1 for children. The admission receipts were $1180. How many adults and how many children attended?

A)330 adults and 190 children
B)190 adults and 330 children
C)295 adults and 225 children
D)95 adults and 425 children

Question 72

Solve the problem.
A merchant has coffee worth $20 a pound that she wishes to mix with 30 pounds of coffee worth $90 a pound to get a mixture that can be sold for $50 a pound. How many pounds of the $20 coffee should be used?

A)40 lb
B)70 lb
C)35 lb
D)20 lb

Question 73

Solve the problem.
A woman made a deposit of $341. If her deposit consisted of 101 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A)41 one-dollars
B)36 one-dollars
C)60 one-dollars
D)31 one-dollars

Question 74

Solve the problem using the elimination method.
The sum of two numbers is 33. The larger number minus the smaller number is 9. What are the numbers?

A)21 and 12
B)25 and 8
C)19 and 14
D)14 and 23

Question 75

Solve the problem.
Andy has 17 coins made up of quarters and half dollars, and their total value is $4.75. How many quarters does he have?

A)4 quarters
B)2 quarters
C)15 quarters
D)20 quarters

Question 76

Solve the problem using the elimination method.
The sum of two numbers is 96. The second number is three times as large as the first number. What are the numbers?

A)22 and 74
B)24 and 72
C)21 and 75
D)22 and 66

Question 77

Solve the problem.
Ron and Kathy are ticket-sellers at their class play, Ron handling student tickets that sell for $2.00 each and Kathy selling adult tickets for $5.50 each. If their total income for 26 tickets was $118.50, how many did Ron sell?

A)9 tickets
B)24 tickets
C)19 tickets
D)7 tickets

Question 78

Solve the problem using the elimination method.
In a basketball game, Will scored 35 points, consisting only of three-point shots and two-point shots. He made a total of 15 shots. How many shots of each type did he make?

A)two-point shots: 10; three-point shots: 5
B)two-point shots: 11; three-point shots: 4
C)two-point shots: 9; three-point shots: 6
D)two-point shots: 5; three-point shots: 10

Question 79

Solve the problem.
Mardi received an inheritance of $70,000. She invested part at 10% and deposited the remainder in tax-free bonds at 8%. Her total annual income from the investments was $6200. Find the amount invested at 10%.

A)$15,000
B)$30,000
C)$63,800
D)$29,000

Question 80

Solve the problem.
In a chemistry class, 9 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

A)5.5 L
B)4.5 L
C)3.5 L
D)9.0 L