Deck 9: Systems of Equations and Inequalities

Question 1

Solve using any method.

A)
B)
C)
D) inconsistent
E)

Answer 1

Question 2

Solve the system by the method of substitution.

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

Answer 2

(4, -3)

Question 3

Solve the system by the method of elimination.

A) inconsistent
B)
C)
D)
E)

Answer 3

Question 4

Solve the system by the method of elimination.

A)
B) (dependent)
C)
D) inconsistent
E)

Question 5

Find the least squares regression line for the points by solving the system for a and b. Points: space

A) y = 3.93x -4.21
B) y = 2.80x -3.20
C) y = -2.66x +2.80
D) y = -3.47x -4.21
E) y = -3.20x +2.80

Question 6

During one performance of a local arts council's presentation of Fiddler on the Roof, the box office sold 200 tickets and collected $1372. If adult tickets sold for $8 and children's tickets sold for $6, how many of each type of ticket were sold?

A) adult tickets sold = 86; children's tickets sold = 114
B) adult tickets sold = 97; children's tickets sold = 125
C) adult tickets sold = 114; children's tickets sold = 86
D) adult tickets sold = 97; children's tickets sold = 99
E) adult tickets sold = 125; children's tickets sold = 97

Question 7

Solve using any method.

A)
B)
C) inconsistent
D)
E)

Question 8

An airplane flying into a headwind travels 216 miles in 2 hours and 42 minutes. On the return flight, the distance is traveled in 2 hours. Find the airspeed of the plane and the speed of the wind, assuming that both remain constant.

A) plane speed = 71 mph; wind speed = 83 mph
B) plane speed = 109 mph; wind speed = 14 mph
C) plane speed = 94 mph; wind speed = 14 mph
D) plane speed = 71 mph; wind speed = 14 mph
E) plane speed = 109 mph; wind speed = 101 mph

Question 9

Use a graphing utility to solve the system of equations. Find the solution accurate to two decimal places.

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

Question 10

Determine which ordered pair is a solution of the system.

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

Question 11

Find the dimensions of the rectangle meeting the specified conditions. The perimeter is 68 centimeters and the length is 2 centimeters more than the width.

A)
B)
C)
D)
E)

Question 12

Solve the system by the method of substitution.

A) no real solution
B) (-4, -25), (5, -16)
C) (-4, -23), (5, -14)
D) (-4, 15), (5, 24)
E) (-4, -25)

Question 13

Find the sales necessary to break even (R - C = 0) for the cost C of producing x units and the revenue R obtained by selling x units. (Round to the nearest whole unit.)

A) 782 units or 852 units
B) 852 units
C) no real solution
D) 782 units
E) 831 units

Question 14

Solve the system by the method of elimination.

A) inconsistent
B)
C)
D)
E)

Question 15

Find the equilibrium point of the demand and supply equations. (The equilibrium point is the price p and number of units x that satisfy both the demand and supply equations.)

A)
B)
C) inconsistent
D)
E)

Question 16

Determine which ordered pair is a solution of the system.

A) (-7,-3)
B) (-4, -6)
C) (-7, 1)
D) (6, 4)
E) (6, -4)

Question 17

The sales of various types of lawn and garden tools vary according to the season. At a certain home improvement store, the monthly sales H of garden hoes (hoes sold per month) declines from July to October whereas the monthly sales of lawn rakes R (rakes sold per month) increase during this same interval. The sales of these two items during the calendar months July-October are modeled by the equations: where t is the month (t = 7 corresponds to July). In which month does the number of rakes sold equal the number of hoes sold?

A) September
B) October
C) July
D) August
E) November

Question 18

Solve the system by the method of substitution.

A) (7, -5), (-7, 5)
B) (7, -5)
C) (0, 7)
D) (0, 0)
E) no real solution

Question 19

Solve the system by the method of elimination.

A)
B)
C)
D) inconsistent
E)

Question 20

Solve the system by the method of substitution.

A) (5, 102), (3, 56), (1, 18)
B) no real solution
C) (-3, -34), (1, 18)
D) (5, 102), (-3, -34), (0, 2)
E) (5, 102), (-1, -12)

Question 21

Solve the system of linear equations.

A)
B)
C)
D)
E) inconsistent

Question 22

A residential building contractor borrowed $30,000 to complete a new home. Some of the money was borrowed at 5%, some at 6%, and some at 8%. How much was borrowed at each rate if the annual interest owed was $1780 and the amount borrowed at 6% is four times more than the amount borrowed at 8%?

A) $8000 at 5%; $18,000 at 6%; $4000 at 8%
B) $10,000 at 5%; $16,000 at 6%; $4000 at 8%
C) $9000 at 5%; $14,000 at 6%; $6000 at 8%
D) $8000 at 5%; $17,000 at 6%; $5000 at 8%
E) $7000 at 5%; $20,000 at 6%; $5000 at 8%

Question 23

Solve the system of linear equations.

A)
B)
C)
D)
E)

Question 24

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

A)
B)
C)
D)
E)

Question 25

Find the equation of the circle that passes through the points .

A)
B)
C)
D)
E)

Question 26

Write the partial fraction decomposition of the rational expression.

A)
B)
C)
D)
E)

Question 27

Use back-substitution to solve the system of linear equations.

A)
B)
C)
D)
E)

Question 28

Write the partial fraction decomposition of the improper rational expression.

A)
B)
C)
D)
E)

Question 29

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

A)
B)
C)
D)
E)

Question 30

Write the partial fraction decomposition of the rational expression.

A)
B)
C)
D)
E)

Question 31

Write the partial fraction decomposition of the improper rational expression.

A)
B)
C)
D)
E)

Question 32

Write the partial fraction decomposition of the rational expression.

A)
B)
C)
D)
E)

Question 33

Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

A)
B)
C)
D)
E)

Question 34

Determine which one of the ordered triples below is a solution of the given system of equations.

A)
B)
C)
D)
E)

Question 35

Write the partial fraction decomposition of the rational expression.

A)
B)
C)
D)
E)

Question 36

An object moving vertically is at the given heights at the specified times. Find the position equation for the object. At t = 1 second, s = 161 feet
At t = 2 seconds, s = 98 feet
At t = 3 seconds, s = 3 feet

A)
B)
C)
D)
E)

Question 37

Applying Kirchhoff's Laws to the electrical network in the figure, the currents I₁, I₂, and I₃ are the solution of the system Find the currents.

A)
B)
C)
D)
E)

Question 38

Solve the system of linear equations.

A)
B)
C)
D)
E)

Question 39

Solve the system of linear equations.

A)
B)
C)
D) inconsistent
E)

Question 40

Find the equation of the parabola that passes through the points.

A)
B)
C)
D)
E)

Question 41

Sketch the graph of the inequality.

A)
B)
C)
D)
E)

Question 42

Use a graphing utility to graph the inequality. Shade the region representing the solution.

A)
B)
C)
D)
E)

Question 43

Write an inequality for the shaded region shown in the figure.

A)
B)
C)
D)
E)

Question 44

Use a graphing utility to graph the inequalities. Shade the region representing the solution set of the system.

A)
B)
C)
D)
E)

Question 45

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

A) (0, 1)
B) (5, -3)
C) (-8, -5)
D) (3, -3)
E) (5, 3)

Question 46

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints.

A)
B)
C)
D)
E)

Question 47

Find the minimum and maximum values of the objective function and where they occur, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.)

A)
B)
C)
D)
E)

Question 48

Derive a set of inequalities to describe the region. Triangle: vertices at (0, 0), (3, 0), (3, 4)

A)
B)
C)
D)
E)

Question 49

For the given supply and demand equations, find the consumer surplus.

A) $10,742,188
B) $5,859,375
C) $11,718,750
D) $9,765,625
E) $14,648,438

Question 50

Sketch the graph and label the vertices of the solution set of the system of inequalities. Shade the solution set.

A)
B)
C)
D)
E)

Question 51

Determine which one of the ordered pairs below is a solution of the system of linear inequalities.

A) (0, 0)
B) (-1, 4)
C) (3, -3)
D) (-9, 7)
E) (9, 6)

Question 52

An investor has $150,000 to invest in two types of investments. Type A pays 5% annually and type B pays 6% annually. To have a well-balanced portfolio, the investor imposes the following conditions. At least one-third of the total portfolio is to be allocated to type A investments and at least one-third of the portfolio is to be allocated to type B investments. What is the optimal amount that should be invested in each investment?

A) $60,000 in type A (5%), $90,000 in type B (6%)
B) $0 in type A (5%), $150,000 in type B (6%)
C) $150,000 in type A (5%), $0 in type B (6%)
D) $100,000 in type A (5%), $50,000 in type B (6%)
E) $50,000 in type A (5%), $100,000 in type B (6%)

Question 53

Derive a set of inequalities to describe the region.

A)
B)
C)
D)
E)