Deck 3: Systems of Linear Equations and Inequalities

Question 1

Solve by using the substitution method.

A) (1, -8)
B) (2, -7)
C) (5, -4)
D) (3, -6)

Answer 1

D

Question 2

Solve by using the substitution method.

A) (-5, 10)
B) (-3, 6)
C) (-8, 16)
D) No solution; { }; inconsistent system

Answer 2

A

Question 3

Solve the system of equations by graphing.

Answer 3

Question 4

Solve the system of equations by graphing.

Question 5

The graph of a system of linear equations is given. Identify the number of solutions to the system.

A) 0
B) 1
C) infinite number of solutions

Question 6

Write the word or phrase that best completes each statement or answers the question.
Solve the system of equations by graphing.

Question 7

Use a graphing calculator to graph each linear equation on the same viewing window. Use a TRACE or INTERSECT feature to find the point of intersection.

A) (12, 10)
B) (10, 5)
C) (15, 13)
D) (5, -3)

Question 8

Solve by using the substitution method.

A) (-3, 0)
B) (0, 3)
C) (0, -3)
D) (3, 0)

Question 9

Determine which point is the solution to the given system.

A) (12, -10)
B) (10, -3)
C) (8, 4)
D) (15, 1)

Question 10

The graph of a system of linear equations is given. Identify whether the system is dependent or independent.

A) independent
B) dependent

Question 11

Find C and D such that the solution set to the system is {(5,4)}.

A) C = 2; D = 6
B) C = 4; D = 5
C) C = 6; D = 2
D) C = 5; D = 4

Question 12

Solve by using the substitution method.

A) (14, -1)
B) (12, -14)
C) (4, -6)
D) Infinitely many solutions; ; dependent system

Question 13

Solve the system of equations by graphing.

Question 14

Solve by using the substitution method.

A) (1, -6)
B) (7, -36)
C) (-1, 4)
D) No solution; { }; inconsistent system

Question 15

Determine which point is the solution to the given system. y = 3x + 22
Y = 2x + 15

A) (5, 37)
B) (-6, 4)
C) (-2, 16)
D) (-7, 1)

Question 16

The graph of a system of linear equations is given. Identify whether the system is consistent or inconsistent.

A) inconsistent
B) consistent

Question 17

Solve the system of equations by graphing.

Question 18

Solve the system by using the substitution method.

A) (19, -12)
B) (4, 15)
C) (14, -3)
D) (9, 6)

Question 19

Solve the system of equations by graphing.

Question 20

Solve the system by using the substitution method.

Question 21

Solve by using either the addition method or the substitution method.

A) (40, 30)
B) (70, 60)
C) (70, 30)
D) (60, 40)

Question 22

Solve the system by the addition method.

Question 23

Solve the system by the addition method. 3x + 7y = -20
-3x + 6y = -6

A) (-9, 1)
B) (5, -5)
C) (-2, -2)
D) (4, 1)

Question 24

Solve the system by using the substitution method.

A) (0, 1)
B) (6, -1)
C) (3, 0)
D) No solution; { }; inconsistent system

Question 25

Solve by using either the addition method or the substitution method.

Question 26

The cost to rent an apartment at Glendale Lakes is $950 per month plus a one-time fee of $300. An
apartment at the Breakers requires a $500 pet fee plus $925 per month.
a. Write the cost y to rent for x months for each apartment.
b. Find the number of months for which the total amount spent for each apartment would be the
same for renters with pets.

Question 27

Solve the system by the addition method.

Question 28

Solve the system by the addition method.

Question 29

Solve the system by the addition method.

Question 30

Solve the system.

Question 31

Solve the system by the addition method.

Question 32

Question 33

Solve the system by the addition method.

Question 34

Solve the system by the addition method.

Question 35

Solve by using either the addition method or the substitution method.

A) (-2, -6)
B) (-5, -4)
C) (-7, -9)
D) (-9, -14)

Question 36

Solve by using either the addition method or the substitution method.

Question 37

Write the word or phrase that best completes each statement or answers the question.
The centroid of a region is the geometric center. For the region shown, the centroid is the point of
intersection of the diagonals of the parallelogram. a. Find the slope-intercept form of the line through the points (3, -6) and (1, 0).
b. Find the slope-intercept form of the line through the points (-1, -1) and (5, -5).
c. Find the centroid of the region.

Question 38

Question 39

Solve the system by using the substitution method.

A) (7, 1540)
B) (9, -160)
C) (4, 340)
D) (5, 740)

Question 40

Solve the system by the addition method.

Question 41

To reach a sales meeting, Carrie traveled by plane for 1 hour and by car for an additional 2 hours. The plane travels 82 mph faster than the car. If the total distance traveled is 217 miles, what are the
Speeds of the plane and the car? (Assume that the plane and the car travel at constant rates.)

A) plane: 132 mph; car: 40 mph
B) plane: 122 mph; car: 50 mph
C) plane: 117 mph; car: 35 mph
D) plane: 127 mph; car: 45 mph

Question 42

Lorenzo invested $22,000 into two accounts; one pays 4% simple interest and the other pays 7% simple interest. At the end of the first year, Lorenzo's total return was $1150. How much did he
Invest in each account?

A) $13,000 at 4%; $9000 at 7%
B) $9000 at 4%; $13,000 at 7%
C) $10,000 at 4%; $12,000 at 7%
D) $12,000 at 4%; $10,000 at 7%

Question 43

Paula invested into two accounts; one pays 7% simple interest and the other pays 8% simple interest. She invested $2000 more in the account paying 8% than in the account paying 7%. At the
End of the first year, Paula's total return was $1810. How much did she invest in each account?

A) $14,000 at 7%; $10,000 at 8%
B) $11,000 at 7%; $13,000 at 8%
C) $13,000 at 7%; $11,000 at 8%
D) $10,000 at 7%; $14,000 at 8%

Question 44

A chemist wants to mix a 23% acid solution with a 43% acid solution to get 15 L of a 31% acid solution. How many liters of the 23% solution and how many liters of the 43% solution should be
Mixed?

A) 5 L of the 23% solution; 10 L of the 43% solution
B) 9 L of the 23% solution; 6 L of the 43% solution
C) 10 L of the 23% solution; 5 L of the 43% solution
D) 6 L of the 23% solution; 9 L of the 43% solution

Question 45

A plane flew 450 miles in 3 hours with the wind. It took 5 hours to travel the same distance against the wind. What is the rate of the plane in still air and the rate of the wind?

A) plane: 150 mph; wind: 90 mph
B) plane: 120 mph; wind: 30 mph
C) plane: 130 mph; wind: 40 mph
D) plane: 130 mph; wind: 30 mph

Question 46

Question 47

Decide which inequality symbol (<, >, , ) should be used by looking at the graph. x - y 2

Question 48

The Walnut Cove Ruritan Club sells hot dogs and drinks from a concession stand at the annual 4th of July parade. Carl bought 6 hot dogs and 4 drinks and paid $17.00. Susan purchased 3 hot dogs
And 4 drinks and was charged $12.50. What is the cost of 1 hot dog and what is the cost of 1 drink?

A) $1.50 for a hot dog; $2.00 for a drink
B) $2.00 for a hot dog; $1.50 for a drink
C) $1.60 for a hot dog; $1.85 for a drink
D) $1.40 for a hot dog; $2.15 for a drink

Question 49

Two trains leave the depot at the same time, one traveling east and the other traveling west. The speed of one train is 14 mph slower than the other. If after 3 hours the distance between the trains is
150 miles, find the speed of each train.

A) 18 mph; 32 mph
B) 17 mph; 33 mph
C) 20 mph; 30 mph
D) 19 mph; 31 mph

Question 50

Identify the inequalities that match the given graph.

Question 51

It takes a barge 1 hour to travel 8 miles downstream with the current and 4 hours to return against the current. Find the speed of the barge in still water and the speed of the current.

A) barge: 8 mph; current: 2 mph
B) barge: 5 mph; current: 3 mph
C) barge: 6 mph; current: 4 mph
D) barge: 6 mph; current: 3 mph

Question 52

A rectangle has the perimeter of 24 inches. The length is 4 in longer than the width. Find the dimensions of the rectangle.

A) 2 inches by 6 inches
B) 7 inches by 11 inches
C) 5 inches by 9 inches
D) 4 inches by 8 inches

Question 53

An isosceles triangle has two angles of the same measure (see figure). If the angle represented by y measures 60° more than the angle x, find the measures of all angles of the triangle.
(Recall that the sum of the measures of the angles of a triangle is 180°.) [Figure is not necessarily drawn to scale.]

A) 37°; 37°; 97°
B) 35°; 35°; 110°
C) 45°; 45°; 90°
D) 40°; 40°; 100°

Question 54

In a right triangle, one acute angle measures 30° more than 4 times the other. If the sum of the measures of the two acute angles must equal 90°, find the measures of the acute angles.

A) 12°, 78°
B) 14°, 76°
C) 11°, 79°
D) 13°, 82°

Question 55

A total of $4.80 consisting of dimes and quarters was collected from a soft drink vending machine. If there are 1 more quarters than dimes, find the number of dimes and the number of quarters.

A) 12 dimes; 13 quarters
B) 14 dimes; 15 quarters
C) 18 dimes; 12 quarters
D) 13 dimes; 14 quarters

Question 56

The Hillsville Little Theater is currently presenting a new stage production of the animated feature Hoodwinked. At the opening, 70 tickets were sold and ticket sales totaled $672. If adult tickets cost
$12 and children's tickets cost $8, how many of each type of ticket were sold?

A) 28 adult tickets; 42 child tickets
B) 26 adult tickets; 44 child tickets
C) 27 adult tickets; 43 child tickets
D) 25 adult tickets; 45 child tickets

Question 57

Question 58

Question 59

One angle measures 66° more than 2 times another. If the two angles are complementary, find the measures of the angles.

A) 10°; 80°
B) 18°; 72°
C) 13°; 77°
D) 8°; 82°

Question 60

Nail polish remover is essentially a mixture of water and a chemical called acetone. How much pure acetone must be combined with a solution that is 10% acetone to make 30 oz of a 37% solution?

A) 15 oz
B) 9 oz
C) 21 oz
D) 14 oz

Question 61

Graph the solution set of the inequality.

Question 62

Graph the solution set of the compound inequality.

Question 63

Graph the solution set of the inequality.

Question 64

Graph the solution set of the inequality.

Question 65

Graph of the solution set of the inequality.

Question 66

Graph the solution set of the compound inequality.

Question 67

Write the word or phrase that best completes each statement or answers the question.
Graph the solution set of the compound inequality.

Question 68

Graph the solution set of the inequality.

Question 69

Graph the solution set of the compound inequality.

Question 70

Graph of the solution set of the inequality.

Question 71

Graph the solution set of the inequality.

Question 72

Graph the solution set of the inequality.

Question 73

Graph the solution set of the inequality.

Question 74

Graph the solution set of the inequality.

Question 75

Graph the solution set of the compound inequality.

Question 76

Graph the solution set of the compound inequality.

Question 77

Graph the solution set of the compound inequality.

Question 78

Write the word or phrase that best completes each statement or answers the question.
Graph the solution set of the compound inequality.

Question 79

Write the word or phrase that best completes each statement or answers the question.
Graph the solution set of the inequality.

Question 80

Write the word or phrase that best completes each statement or answers the question.
Graph the solution set of the inequality.