Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
1
A.REI.C.6: Graphing Linear Systems
1 Rowan has $50 in a savings jar and is putting in $5
every week. Jonah has $10 in his own jar and is
putting in $15 every week. Each of them plots his
progress on a graph with time on the horizontal
axis and amount in the jar on the vertical axis.
Which statement about their graphs is true?
1) Rowan’s graph has a steeper slope than
Jonah’s.
2) Rowan’s graph always lies above Jonah’s.
3) Jonah’s graph has a steeper slope than
Rowan’s.
4) Jonah’s graph always lies above Rowan’s.
2 What is the solution of the system of equations
shown in the graph below?
1)
(1,0)
and
(
−
3,0)
2)
(0,
−
3)
and
(0,
−
1)
3)
(
−
1
,
−
2
)
4)
(
−
2
,
−
1
)
3 A system of equations is graphed on the set of axes
below.
The solution of this system is
1)
(
0
,
4
)
2)
(
2
,
4
)
3)
(
4
,
2
)
4)
(
8
,
0
)
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
2
4 On the set of axes below, solve the following
system of equations graphically. State the
coordinates of the solution.
y = 4x − 1
2x + y = 5
5 On the grid below, solve the system of equations
graphically for x and y.
4x − 2y = 10
y = −2x − 1
6 Two health clubs offer different membership plans.
The graph below represents the total cost of
belonging to Club A and Club B for one year.
If the yearly cost includes a membership fee plus a
monthly charge, what is the membership fee for
Club A? What is the number of the month when
the total cost is the same for both clubs? What is
the total cost for Club A when both plans are the
same? What is the monthly charge for Club B?
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
3
7 Two video rental clubs offer two different rental
fee plans: Club A charges $12 for membership and
$2 for each rented video. Club B has a $4
membership fee and charges $4 for each rented
video. The graph below represents the total cost of
renting videos from Club A.
(a) On the same set of xy-axes, draw a line to
represent the total cost of renting videos from Club
B.
(b) For what number of video rentals is it less
expensive to belong to Club A? Explain how you
arrived at your answer.
8 At Ron’s Rental, a person can rent a big-screen
television for $10 a month plus a one-time
“wear-and-tear” fee of $100. At Josie’s Rental, the
charge is $20 a month and an additional charge of
$20 for delivery with no “wear-and-tear” fee.
a If c equals the cost, write one equation
representing the cost of the rental for m months at
Ron’s Rental and one equation representing the
cost of the rental for m months at Josie’s Rental.
b On the accompanying grid, graph and label each
equation.
c From your graph, determine in which month
Josie’s cost will equal Ron’s cost.
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
4
9 Lydia wants to take art classes. She compares the
cost at two art centers. Center A charges $25 per
hour and a registration fee of $25. Center B
charges $15 per hour and a registration fee of $75.
Lydia plans to take x hours of classes. Write an
equation that models this situation, where A
represents the total cost of Center A. Write an
equation that models this situation, where B
represents the total cost of Center B. If Lydia
wants to take 10 hours of classes, use your
equations to determine which center will cost less.
Graph your equations for Center A and Center B on
the set of axes below.
State the number of hours of classes when the
centers will cost the same.
10 Next weekend Marnie wants to attend either
carnival A or carnival B. Carnival A charges $6 for
admission and an additional $1.50 per ride.
Carnival B charges $2.50 for admission and an
additional $2 per ride.
a) In function notation, write
A(x)
to represent the
total cost of attending carnival A and going on x
rides. In function notation, write
B(x)
to represent
the total cost of attending carnival B and going on x
rides.
b) Determine the number of rides Marnie can go on
such that the total cost of attending each carnival is
the same. [Use of the set of axes below is
optional.]
c) Marnie wants to go on five rides. Determine
which carnival would have the lower total cost.
Justify your answer.
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
5
11 A local business was looking to hire a landscaper
to work on their property. They narrowed their
choices to two companies. Flourish Landscaping
Company charges a flat rate of $120 per hour.
Green Thumb Landscapers charges $70 per hour
plus a $1600 equipment fee. Write a system of
equations representing how much each company
charges. Determine and state the number of hours
that must be worked for the cost of each company
to be the same. [The use of the grid below is
optional.] If it is estimated to take at least 35 hours
to complete the job, which company will be less
expensive? Justify your answer.
12 Currently, Tyrone has $60 and his sister has $135.
Both get an allowance of $5 each week. Tyrone
decides to save his entire allowance, but his sister
spends all of hers each week plus an additional $10
each week. After how many weeks will they each
have the same amount of money? [The use of the
grid is optional.]
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
6
13 Island Rent-a-Car charges a car rental fee of $40
plus $5 per hour or fraction of an hour. Wayne’s
Wheels charges a car rental fee of $25 plus $7.50
per hour or fraction of an hour. Under what
conditions does it cost less to rent from Island
Rent-a-Car? [The use of the accompanying grid is
optional.]
14 Franco and Caryl went to a bakery to buy desserts.
Franco bought 3 packages of cupcakes and 2
packages of brownies for $19. Caryl bought 2
packages of cupcakes and 4 packages of brownies
for $24. Let x equal the price of one package of
cupcakes and y equal the price of one package of
brownies. Write a system of equations that
describes the given situation. On the set of axes
below, graph the system of equations.
Determine the exact cost of one package of
cupcakes and the exact cost of one package of
brownies in dollars and cents. Justify your
solution.
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
7
15 Central High School had five members on their
swim team in 2010. Over the next several years,
the team increased by an average of 10 members
per year. The same school had 35 members in their
chorus in 2010. The chorus saw an increase of 5
members per year. Write a system of equations to
model this situation, where x represents the number
of years since 2010. Graph this system of
equations on the set of axes below.
Explain in detail what each coordinate of the point
of intersection of these equations means in the
context of this problem.
16 A recreation center ordered a total of 15 tricycles
and bicycles from a sporting goods store. The
number of wheels for all the tricycles and bicycles
totaled 38. Write a linear system of equations that
models this scenario, where t represents the number
of tricycles and b represents the number of bicycles
ordered. On the set of axes below, graph this
system of equations.
Based on your graph of this scenario, could the
recreation center have ordered 10 tricycles?
Explain your reasoning.
Regents Exam Questions A.REI.C.6: Graphing Linear Systems Name: ________________________
www.jmap.org
8
17 Two families went to Rollercoaster World. The
Brown family paid $170 for 3 children and 2
adults. The Peckham family paid $360 for 4
children and 6 adults. If x is the price of a child's
ticket in dollars and y is the price of an adult's
ticket in dollars, write a system of equations that
models this situation. Graph your system of
equations on the set of axes below.
State the coordinates of the point of intersection.
Explain what each coordinate of the point of
intersection means in the context of the problem.
ID: A
1
A.REI.C.6: Graphing Linear Systems
Answer Section
1 ANS: 3
15 > 5
REF: 081502ai
2 ANS: 3 REF: 011304ia
3 ANS: 3 REF: 081201ia
4 ANS:
REF: 011235ia
5 ANS:
REF: 080938ia
6 ANS:
$50, 5, $125, $10.
.
REF: 089935a
ID: A
2
7 ANS:
. It is less expensive to rent 5 or more videos from Club A, as indicated from the graph
above.
REF: spring9831a
8 ANS:
a) Ron:
c = 10m + 100
, Josie:
c = 20m + 20
; b) c) 8
REF: 060232a
ID: A
3
9 ANS:
a = 25x + 25
b = 15x + 75
;
a = 25(10) + 25 = 275
b = 15(10) + 75 = 225
b will cost less; ; 5 hours
REF: 082337ai
10 ANS:
a)
A(x) = 1.50x + 6
B(x) = 2x + 2.50
b)
1.50x + 6 = 2x + 2.50
.50x = 3.50
x = 7
c)
A(x) = 1.50(5) + 6 = 13.50
B(x) = 2(5) + 2.50 = 12.50
Carnival B has a lower cost.
REF: spr1308ai
ID: A
4
11 ANS:
y = 120x
and
y = 70x + 1600
120x = 70x + 1600
50x = 1600
x = 32
y = 120(35) = 4200
y = 70(35) + 1600 = 4050
Green Thumb is less expensive.
REF: fall1315ai
12 ANS:
5.
.
REF: 010329a
ID: A
5
13 ANS:
h > 6
. .
REF: 060226b
14 ANS:
3x + 2y = 19
2x + 4y = 24
6x + 4y = 38
2x + 4y = 24
4x = 14
x = 3.50
2(3.50) + 4y = 24
7 + 4y = 24
4y = 17
y = 4.25
REF: 061637ai
15 ANS:
y = 10x + 5
y = 5x + 35
In 2016, the swim team and chorus will each have 65 members.
REF: 061737ai
ID: A
6
16 ANS:
t + b = 15
3t + 2b = 38
No, because according to the graph, 8 tricycles were ordered.
REF: 011937ai
17 ANS:
3x + 2y = 170
4x + 6y = 360
(30,40) The price of a child’s ticket is $30 and the price of an adult’s
ticket is $40.
REF: 012037ai
