Deck 4: Systems of Equations

Question 1

Write the word or phrase that best completes each statement or answers the question.

Answer 1

B

Question 2

Write the word or phrase that best completes each statement or answers the question.

Answer 2

D

Question 3

Is the ordered pair a solution of the given system of equations?
(-3, -1), 3x + y = -8 4x + 3y = -9

A) Yes
B) No

Answer 3

B

Question 4

Write the word or phrase that best completes each statement or answers the question.

Question 5

Write the word or phrase that best completes each statement or answers the question.

Question 6

Is the ordered pair a solution of the given system of equations?
A student was asked to find ordered pairs that solve the system of equations x + 2y = 3
-2x - 4y = -6.
The student claims that (1, 1) and (-1, 2) are the only solutions. Is the student correct?

A) Yes
B) No

Question 7

Write the word or phrase that best completes each statement or answers the question.
x + 9y = 9 6x - 5y = -5

A) (0, 0)
B) (1, 1)
C) (0, 1)
D) (1, 0)

Question 8

Is the ordered pair a solution of the given system of equations?
(2, 1), 3x + y = 7 2x + 3y = 7

A) Yes
B) No

Question 9

Is the ordered pair a solution of the given system of equations?
(5, -2), 3x - y = 17 4x - 3y = 26

A) Yes
B) No

Question 10

Write the word or phrase that best completes each statement or answers the question.
3x + y = 13 2x + 9y = -8

A) (5, 2)
B) (5, -2)
C) (-5, 2)
D) (-5, -2)

Question 11

Write the word or phrase that best completes each statement or answers the question.
Explain why the solution of a system of equations is the point of intersection of the graphs
of the equations.

Question 12

Is the ordered pair a solution of the given system of equations?
(4, 6), 3x - y = -6 4x - 3y = 2

A) Yes
B) No

Question 13

Is the ordered pair a solution of the given system of equations?
(1, -6), x + y = -7 x - y = 5

A) Yes
B) No

Question 14

Write the word or phrase that best completes each statement or answers the question.
Describe the three possible outcomes when graphing a system of equations, and relate
each to the type of solution(s) each system has.

Question 15

Is the ordered pair a solution of the given system of equations?
If the y term is missing in

A) Parallel
B) Parallel or One Graph
C) Intersecting
D) One Graph

Question 16

Write the word or phrase that best completes each statement or answers the question.

Question 17

Is the ordered pair a solution of the given system of equations?
(-1, 3), xx -+ yy == -24

A) Yes
B) No

Question 18

Write the word or phrase that best completes each statement or answers the question.

Question 19

Write the word or phrase that best completes each statement or answers the question.

Question 20

Write the word or phrase that best completes each statement or answers the question.

Question 21

Write the word or phrase that best completes each statement or answers the question.
True or False? When graphing a linear inequality, the origin can always be used as a test point for
determining which side of a boundary line should be shaded.

Question 22

Write the word or phrase that best completes each statement or answers the question.
x + y = -4 x + y = -5

A) (0, -9)
B) (-4 -5)
C) (0, 0)
D)

Question 23

Write the word or phrase that best completes each statement or answers the question.
Under what condition(s) will a system of two linear inequalities have no solution?

Question 24

Write the word or phrase that best completes each statement or answers the question.
True or False? A system of two linear inequalities can have solutions in all quadrants.

Question 25

Write the word or phrase that best completes each statement or answers the question.
x - 5y = -4 x + 8y = -4

A) (0, -4)
B) (-4, 0)
C) (0, 4)
D) (4, 0)

Question 26

Write the word or phrase that best completes each statement or answers the question.
True or False? Every system of two linear inequalities has infinitely many solutions.

Question 27

Write the word or phrase that best completes each statement or answers the question.
5x + 3y = 80 2x + y = 30

A) (10, 0)
B) (0, 0)
C) (0, 10)
D) (10, 10)

Question 28

Write the word or phrase that best completes each statement or answers the question.
5x - 2y = -1 x + 4y = 35

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

Question 29

Solve the problem.
In a recent school board election, the two candidates for president received 3064 votes. The loser received 608 fewer votes than the winner. How many votes did the winner receive?

A) 1836 votes
B) 1222 votes
C) 2456 votes
D) 1228 votes

Question 30

Write the word or phrase that best completes each statement or answers the question.

Question 31

Write the word or phrase that best completes each statement or answers the question.
True or False? A system of two linear inequalities can have solutions in only one quadrant.

Question 32

Write the word or phrase that best completes each statement or answers the question.
True or False? It is impossible for a system of two linear inequalities to have exactly one solution.

Question 33

Write the word or phrase that best completes each statement or answers the question.

Question 34

Solve the problem.

A) 11 dimes
B) 8 dimes
C) 34 dimes
D) 23 dimes

Question 35

Solve the problem.
There were 550 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $830. How many adults and how many children attended?

A) 207 adults and 343 children
B) 270 adults and 280 children
C) 135 adults and 415 children
D) 280 adults and 270 children

Question 36

Write the word or phrase that best completes each statement or answers the question.

Question 37

Write the word or phrase that best completes each statement or answers the question.
True or False? A system of two linear inequalities can have solutions in exactly three of the
quadrants.

Question 38

Write the word or phrase that best completes each statement or answers the question.
x + 7y = -2 3x + y = 34

A) (7, 12)
B) (-2, 3)
C) (3, 7)
D) (12, -2)

Question 39

Solve the problem.
Devon purchased tickets to an air show for 5 adults and 2 children. The total cost was $112. The cost of a childʹs ticket was $7 less than the cost of an adultʹs ticket. Find the price of an adultʹs ticket
And a childʹs ticket.

A) adultʹs ticket: $20; childʹs ticket: $13
B) adultʹs ticket: $18; childʹs ticket: $11
C) adultʹs ticket: $19; childʹs ticket: $12
D) adultʹs ticket: $17; childʹs ticket: $10

Question 40

Write the word or phrase that best completes each statement or answers the question.
True or False? When graphing a system of two linear inequalities, the final shaded region is made
up of all points which belong to the graphs of either of the individual inequalities.

Question 41

Write the word or phrase that best completes each statement or answers the question.

Question 42

Write the word or phrase that best completes each statement or answers the question.
Under what circumstances can a system of equations be solved more easily by graphing
than be substitution?

Question 43

Write the word or phrase that best completes each statement or answers the question.

Question 44

Write the word or phrase that best completes each statement or answers the question.
A student argued that it is impossible to use the substitution method to determine if a
system of equations has no solution or an infinite number of solutions. Is the student
correct?

Question 45

Write the word or phrase that best completes each statement or answers the question.
Give an equation that, along with the equation y = 6x + 1

Question 46

Write the word or phrase that best completes each statement or answers the question.
C)
D)

Question 47

Write the word or phrase that best completes each statement or answers the question.

Question 48

Write the word or phrase that best completes each statement or answers the question.
D)

Question 49

Write the word or phrase that best completes each statement or answers the question.
Solve the following system of equations by first solving Equation (1) for x and then
substituting for x in Equation (2). Then solve the system again by first solving Equation
(1) for 2y and substituting for 2y in Equation (2). Which procedure do you prefer? Explain
why you answered as you did.
x + 2y = 6 (1)
3x + 2y = 4 (2)

Question 50

Write the word or phrase that best completes each statement or answers the question.
Give an equation that, along with the equation y = 3x + 6

Question 51

Solve the problem.
In a certain region, the median age of men, y, at their first marriage in a particular year can be approximated by the equation y = 0.12x + 23.7, where x represents the number of years after 1980
And y is in years. In the same region, the median age of women, y, at their first marriage in a
Particular year can be approximated by the equation y = 0.22x + 21.6, where x represents the
Number of years after 1980 and y is in years. If the current trend continues in this region, in what
Year will the median age of men at their first marriage equal the median age of women at their first
Marriage?

A) 2001
B) 2002
C) 2000
D) 1991

Question 52

Write the word or phrase that best completes each statement or answers the question.
x + y = -6 x + y = -4

A) (-6 -4)
B) (0, -10)
C) Dependent, (x, -10 - x)
D) Inconsistent, ∅

Question 53

Write the word or phrase that best completes each statement or answers the question.
Describe two advantages of the substitution method over the graphing method for solving
systems of equations.

Question 54

Provide an appropriate response.
When solving a system of equations, you get x - 3 = x + 3. How many solutions are there?

A) No solutions
B) One solution
C) Infinitely many

Question 55

Solve the problem.
The number of cars sold by a certain automobile manufacturer, y, in a particular year can be approximated by the equation y = -307x + 27,878, where x represents the number of years after
1990. The number of SUVs sold by the same automobile manufacturer, y, in a particular year can
Be approximated by the equation y = 444x + 19,769, where x represents the number of years after
1990. In what year did this automobile manufacturer sell an equal number of cars and SUVs?

A) 2050
B) 2049
C) 2001
D) 2000

Question 56

Write the word or phrase that best completes each statement or answers the question.
Give an equation that, along with the equation y = 8x + 6

Question 57

Write the word or phrase that best completes each statement or answers the question.

Question 58

Solve the problem.
On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $8 each and a number of necklaces at $15 each. She wrote a check for $1100 to pay for
The order. How many bracelets and how many necklaces did Rosaria purchase?

A) 105 bracelets and 15 necklaces
B) 110 bracelets and 10 necklaces
C) 95 bracelets and 25 necklaces
D) 100 bracelets and 20 necklaces

Question 59

Provide an appropriate response.
Solving for which variable in which equation involves the least amount of work? 5x - 7y = -60
-9x - 3y = 30

A) x in equation 2B)y in equation 1C)y in equation 2D)x in equation 1

Question 60

Write the word or phrase that best completes each statement or answers the question.
A student solved the system of equations
x + 2y = 4
2x + 4y = 8
for x in the first equation, and substituted into the second equation. The yʹs also
disappeared in the process. The student claimed that the system of equations has no
solution. Is this correct?

Question 61

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
Andy has 17 coins made up of quarters and half dollars, and their total value is $5.25. How many quarters does he have?

A) 6 quarters
B) 18 quarters
C) 13 quarters
D) 4 quarters

Question 62

Write the word or phrase that best completes each statement or answers the question.
A store sells televisions for $360 and digital video recorders for $270. At the beginning of the week its entire stock is worth $59,580. During the week it sells three quarters of the televisions and one
Third of the digital video recorders for a total of $34,560. How many televisions and digital video
Recorders did it have in its stock at the beginning of the week?

A) 95 televisions; 94 digital video recorders
B) 98 televisions; 90 digital video recorders
C) 96 televisions; 96 digital video recorders
D) 97 televisions; 93 digital video recorders

Question 63

Write the word or phrase that best completes each statement or answers the question.
South Wind Vineyards uses 830 acres to plant Chardonnay and Riesling grapes. The vintner knows the profits will be greatest by planting 240 more acres of Chardonnay than Riesling. How
Many acres of each grape should be planted?

A) Riesling: 212 acres; Chardonnay: 618 acres
B) Riesling: 295 acres; Chardonnay: 535 acres
C) Riesling: 378 acres; Chardonnay: 452 acres
D) Riesling: 535 acres; Chardonnay: 295 acres

Question 64

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
Write a system of equations that would be more easily solved using the substitution
method than the addition method. Explain why substitution would be easier than
addition.

Question 65

Write the word or phrase that best completes each statement or answers the question.
Adam has a total of 62 coins, all of which are either dimes or nickels. The total value of the coins is $5.35. Find the number of each type of coin.

A) 22 nickels; 40 dimes
B) 19 nickels; 43 dimes
C) 45 nickels; 17 dimes
D) 17 nickels; 45 dimes

Question 66

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
A student tried to clear the fractions in

Question 67

Write the word or phrase that best completes each statement or answers the question.
There were 35,000 people at a ball game in Los Angeles. The dayʹs receipts were $238,000. How many people paid $12 for reserved seats and how many paid $5 for general admission?

A) 19,250 paid $12 and 15,750 paid $5
B) 15,750 paid $12 and 19,250 paid $5
C) 9000 paid $12 and 26,000 paid $5
D) 26,000 paid $12 and 9000 paid $5

Question 68

Write the word or phrase that best completes each statement or answers the question.

Question 69

Write the word or phrase that best completes each statement or answers the question.

Question 70

Write the word or phrase that best completes each statement or answers the question.
A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot dogs and 5 bags of potato chips for $16.75. Another customer buys 2 hot dogs and 3 bags of potato chips for $9.25. Find the
Cost of each item.

A) $2.25 for a hot dog; $2.00 for a bag of potato chips
B) $2.00 for a hot dog; $1.75 for a bag of potato chips
C) $1.75 for a hot dog; $2.00 for a bag of potato chips
D) $2.00 for a hot dog; $2.00 for a bag of potato chips

Question 71

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
While using the addition method, if the following occurs, what can you say about the
graph of the system of equations?
3x - 7y = 8
- 3x + 7y = -8
0 = 0

Question 72

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
Explain how the multiplication and addition principles are used in solving systems of
equations using the addition method.

Question 73

Write the word or phrase that best completes each statement or answers the question.

Question 74

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
A sum of money amounting to $3.10 consists of dimes and quarters. If there are 16 coins in all, how many are quarters?

A) 6 quarters
B) 8 quarters
C) 15 quarters
D) 10 quarters

Question 75

Write the word or phrase that best completes each statement or answers the question.

A) 45 quarters and 51 nickels
B) 91 quarters and 5 nickels
C) 40 quarters and 56 nickels
D) 56 quarters and 40 nickels

Question 76

Write the word or phrase that best completes each statement or answers the question.

Question 77

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32
A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
A woman made a deposit of $278. If her deposit consisted of 74 bills, some of them one-dollar bills and the rest being five-dollar bills, how many one-dollar bills did she deposit?

A) 18 one-dollar bills
B) 23 one-dollar bills
C) 13 one-dollar bills
D) 51 one-dollar bills

Question 78

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
Write a system of equations that would be more easily solved using the addition method
than the substitution method. Explain why addition would be easier than substitution.

Question 79

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
-4x + 5y = A
4x - 3y = B
For what values of A or B can this system of equations have (0, 0) as a solution?

Question 80

work. Do not solve.
-5x + 9y = -12
-4x - 4y = -32

A) Substitution B) Addition
Answer: B
Write the word or phrase that best completes each statement or answers the question.
2x + 3y = -1
4x + 2y = -3
What number would you multiply the top equation by to eliminate the x terms?