Deck 5: Systems of Equations and Inequalities

Question 1

Solve the system of equations by using the addition method.

Answer 1

C

Question 2

Solve the system of equations by using the substitution method.

Answer 2

C

Question 3

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.

A) Yes
B) No

Answer 3

A

Question 4

A system of linear equations in two variables may have infinitely many solutions. In such a case, the
equations are said to be .

Question 5

Solve the system by substitution.

Question 6

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.

A) No
B) Yes

Question 7

Solve the system of equations by using the substitution method.

Question 8

Solve the system of equations by using the addition method.

Question 9

Determine which point is the solution to the given system.

Question 10

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.

A) Yes
B) No

Question 11

Solve the system by substitution.

Question 12

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.

A) Yes
B) No

Question 13

Solve the system by substitution.

Question 14

Two or more linear equations taken together is called a of linear equations.

Question 15

Solve the system by substitution.

Question 16

A system of equations is given in which each question is written in slope-intercept form. Determine the
number of solutions. If the system does not have one unique solution, state whether the system is
inconsistent or whether the equations are dependent.

A) One solution
B) Infinitely many solutions; The equations are dependent.
C) No solution; The system is inconsistent.

Question 17

A system of equations that has no solution is called an system.

Question 18

A system of linear equations in two variables may have no solution. In such a case, the equations
represent lines.

Question 19

Two algebraic methods to solve a system of linear equations in two variables are the
method and the method.

Question 20

A to a system of equations in two variables is an ordered pair that is a solution to
each individual equation in the system.

Question 21

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 22

Solve the system of equations by using the addition method.

Question 23

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 24

Solve the problem.

Question 25

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 26

Solve the problem.
A fishing boat travels 36 mi with the current in 2 hr. It travels 42 mi against the current in 3 hr. Find the speed of the boat in still water.

A) The boat travels 2 mph in still water.
B) The boat travels 14 mph in still water.
C) The boat travels 18 mph in still water.
D) The boat travels 16 mph in still water.

Question 27

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 28

Solve the problem.
The average weekly salary of two employees is $1,200. One makes $200 more than the other. Find their salaries.

A) One makes $700 and the other makes $900.
B) One makes $500 and the other makes $700.
C) One makes $1,100 and the other makes $1,300.
D) One makes $1,300 and the other makes $1,500.

Question 29

Solve the problem.

Question 30

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 31

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 32

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 33

Solve the system of equations by using the addition method.

Question 34

Solve the problem.

Question 35

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 36

Solve the problem.
Camille and Sasha each make an ice cream sundae. Camille gets 2 scoops of Cherry ice cream and 1 scoop of Mint Chocolate Chunk ice cream for a total of 46 g of fat. Sasha has 3 scoops of Cherry ice
Cream and 2 scoop of Mint Chocolate Chunk ice cream for a total of 77 g of fat. How many grams
Of fat does 1 scoop of each type of ice cream have?

A) Cherry has 17 g of fat and Mint Chocolate Chunk has 14 g of fat.
B) Cherry has 14 g of fat and Mint Chocolate Chunk has 17 g of fat.
C) Cherry has 15 g of fat and Mint Chocolate Chunk has 16 g of fat.
D) Cherry has 16 g of fat and Mint Chocolate Chunk has 15 g of fat.

Question 37

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 38

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 39

Solve the problem.
In an open market, the price of an item is dependent on the demand by consumers and the supply offered by producers. Competition between buyers and sellers steers the price toward an equilibrium price--that is,
The price where supply equals demand. The number of items offered and sold at the equilibrium price is the
Equilibrium quantity.

Question 40

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.

Question 41

Find the measure of angles x and y.
(The figure is not necessarily drawn to scale.)

Question 42

Solve the problem.
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 28% acetone to make 24 oz of a 58% solution?

A) 14 oz
B) 12 oz
C) 10 oz
D) 17 oz

Question 43

Solve the problem.

Question 44

Solve the problem.
Find the area of the triangle bounded by the lines , and the x-axis.

A) 4 square units
B) 2 square units
C) 28 square units
D) 14 square units

Question 45

Solve the problem.
To reach a sales meeting, Carrie traveled by plane for 2 hours and by car for an additional 2 hours. The plane travels 54 mph faster than the car. If the total distance traveled is 308 miles, what are the
Speeds of the plane and the car? (Assume that the plane and the car travel at constant rates.)

A) plane: 109 mph; car: 45 mph
B) plane: 104 mph; car: 50 mph
C) plane: 99 mph; car: 55 mph
D) plane: 94 mph; car: 40 mph

Question 46

Determine if the ordered triple is a solution to the system of equations.

B) Yes

Question 47

Use the substitution to rewrite the equations in the system in terms of the variables u and
v. Solve the system in terms of u and v. Then back substitute to determine the solution set to the original
system in terms of x and y.

Question 48

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
An equation of the form (where A, B, and C are not all zero) is called a
equation in three variables.

Question 49

Solve the problem.
Two angles are supplementary. The measure of one angle is 68° more than 3 times the measure of the other angle. Find the measure of each angle.

A) 62° and 118°
B) 107° and 253°
C) 28° and 152°
D) 73° and 287°

Question 50

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A solution to a system of linear equations in three variables is an ordered that satisfies
each equation in the system. Graphically, this is the point of of three planes.

Question 51

Solve the problem.
A vendor at a carnival sells cotton candy and caramel apples for $2.00 each. The vendor is charged $60 to set up his booth. Furthermore, the vendor's average cost for each product he produces is
Approximately $0.80.

A) Write a linear cost function representing the cost C(x) (in $) to produce x products.
B) Write a linear revenue function representing the revenue R(x) (in $) for selling x products.
C) Determine the number of products to be produced and sold for the vendor to break even.

Question 52

Solve the system by substitution.
9x - 5y = 16 y = - 12 x + 6

A) 2023, 12823
B) { }
C) {(-4, -4)}
D) {(4, 4)}

Question 53

Solve the problem.

Question 54

Solve the problem.
A helicopter flies 168 miles against the wind in 2 hours; with the wind, it can fly 252 miles in the same amount of time. Find the speed of the helicopter in still air.

A) 21 miles per hour
B) 63 miles per hour
C) 105 miles per hour
D) 84 miles per hour

Question 55

Solve the problem.
The points shown in the graph represent the per capita consumption of chicken and beef in a country x years after the year 2000. a. Use the given data points to write a linear function that approximates per capita consumption of
Chicken C(x) (in lb) at a time x years since the year 2000.
B) Use the given data points to write a linear function that approximates per capita consumption of
Beef B(x) (in lb) at a time x years since the year 2000.
C) Approximate the solution to the system of linear equations defined by the functions from parts (a)
And (b). Round to 1 decimal place. Interpret the meaning of the solution to the system.

Question 56

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
A solution to a linear equation in three variables is an ordered (x, y, z) that satisfies
the equation.

Question 57

Solve the problem.
Abram and Fred leave opposite ends of a bike trail 8.5 miles apart and travel toward each other. Abram is traveling 3 mph faster than Fred. Find each of their speeds if they meet after 30 minutes.

A) Abram: 17 mph; Fred: 20 mph
B) Abram: 10 mph; Fred: 7 mph
C) Abram: 7 mph; Fred: 10 mph
D) Abram: 20 mph; Fred: 17 mph

Question 58

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The graph of a linear equation in two variables is a line in a two-dimensional coordinate system.
The graph of a linear equation in three variables is a in a three-dimensional
coordinate system.

Question 59

Solve the problem.
One angle measures 27° more than 2 times another. If the two angles are complementary, find the measures of the angles.

A) 26°; 64°
B) 23°; 67°
C) 21°; 69°
D) 31°; 59°

Question 60

Choose the one alternative that best completes the statement or answers the question.
Find three ordered triples that are solutions to the linear equation in three variables.

Question 61

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 62

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 63

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 64

Solve the problem.
A theater charges $50 per ticket for seats in section A, $40 per ticket for seats in section B, and $20 per ticket for seats in section C. For one play, 9,500 tickets were sold for a total of $335,000 in
Revenue. If 500 more tickets in section B were sold than the other two sections combined, how many
Tickets in each section were sold?

A) 3,000 tickets in section A, 5,000 tickets in section B, and 1,500 tickets in section C were sold.
B) 3,000 tickets in section A, 3,500 tickets in section B, and 1,500 tickets in section C were sold.
C) 1,500 tickets in section A, 3,500 tickets in section B, and 3,000 tickets in section C were sold.
D) 1,500 tickets in section A, 5,000 tickets in section B, and 3,000 tickets in section C were sold.

Question 65

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 66

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 67

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 68

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 69

Solve the problem.
A basketball player scored 33 points in one game. In basketball, some baskets are worth 3 points, some are worth 2 points, and free-throws are worth 1 point. He scored four more 2-point baskets
Than he did 3-point baskets. The number of free throws equaled the sum of the number of 2-point
And 3-point shots made. How many free-throws did he make?

A) He made 3 free-throws.
B) He made 7 free-throws.
C) He made 13 free-throws.
D) He made 10 free-throws.

Question 70

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 71

Identify the ordered triple that is a solution to the system.
-2x - 4y - 6z = 16
-8x - 7y + 7z = -2 4x - 3y - 7z = -8

A) (-5, 9, -7)
B) (-11, 3, -1)
C) (-5, 3, -3)
D) All three points are solutions to the system.

Question 72

Identify the system for which the ordered triple is a solution.

Question 73

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 74

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 75

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 76

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 77

Solve the problem.
Josie invested $13,000 in three different mutual funds. A fund containing large cap stocks made 5.7% return in 1 yr. A real estate fund lost 12.6% in 1 yr, and a bond fund made 3.5% in 1 yr. The
Amount invested in the large cap stock fund was twice the amount invested in the real estate fund. If
Josie had a net return of $162.50 across all investments, how much did she invest in the large cap
Fund?

A) She invested $8,000 in the large cap fund.
B) She invested $5,000 in the large cap fund.
C) She invested $5,500 in the large cap fund.
D) She invested $2,500 in the large cap fund.

Question 78

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the
number of solutions to the system, and determine whether the system is inconsistent, or the equations are
dependent.

Question 79

Solve the system. If there is more than one solution, write the general solution.

Question 80

Solve the system. If there is more than one solution, write the general solution.