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Name: _______________________________
Period: _____
Review -- Linear Systems
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Use substitution to determine if (0, 2) is an element of the solution set for the system of equations.
a. (0, 2) is not a solution of the system.
____
____
2. Maximize the objective function
b. (0, 2) is a solution of the system.
under the constraints
a. No maximum exists.
c.
b. (10,0)
d. (8, 0)
3. Use elimination to solve the system of equations
a. (14.1, –8.6, –3.2)
b. (5, 0, 4)
____
.
.
c. (–6, –13.2, 0.7)
d. (10, 12, 3)
4. A teacher prepares 3 different tests. The teacher uses 3 types of questions which are each worth a certain
number of points. The table shows the number of questions of each type on each of the three tests. Find the
number of points each type of question is worth.
Test 1
Test 2
Test 3
a.
b.
c.
d.
Question
Type A
36
3
0
Question
Type B
3
45
1
Question
Type C
0
1
39
Total
Points
150
103
41
There is no solution to this problem.
Question type A is worth 1 point, type B is worth 2 points, and type C is worth 4 points.
Question type A is worth 4 points, type B is worth 2 points, and type C is worth 1 point.
Question type A is worth 4 points, type B is worth 48 points, and type C is worth 1 point.
Short Answer
1. Use a graph to solve the system
. Check your answer.
Name: _______________________________
Period: _____
2. Two snow resorts offer private lessons to their customers. Big Time Ski Mountain charges $5 per hour plus
$50 insurance. Powder Hills charges $10 per hour plus $30 insurance. For what number of hours is the cost of
lessons the same for each resort?
3. Jake fills a tank that can hold 200 gallons of water. The tank already has 50 gallons of water in it when Jake
starts filling it at the rate of 10 gallons per minute. Karla fills a tank that can hold 300 gallons of water. That
tank already has 100 gallons of water in it when Karla starts filling it at the rate of 5 gallons per minute. Jake
and Karla start filling the tanks at the same time. How long after they start filling the tanks do the tanks have
the same volume of water? What is that volume of water?
4. Use substitution to solve the system
.
5. Use elimination to solve the system
6. Graph the system of inequalities
.
.
7. Mina’s Catering Service is organizing a formal dinner for at least 280 people. The hall has two kinds of
tables, one that seats 4 people and one that seats 10 people. The hall can contain up to a total of 52 tables.
Write and graph a system of inequalities that can be used to determine the possible combinations of tables that
can be used for the event so there are enough seats for all the people.
8. Graph the system of inequalities, and classify the figure created by the solution region.
9. A shop makes tables and chairs. Each table takes 8 hours to assemble and 2 hours to finish. Each chair takes 3
hours to assemble and 1 hour to finish. The assemblers can work for at most 200 hours each week, and the
finishers can work for at most 60 hours each week. The shop wants to make as many tables and chairs as
possible. Write the constraints for the problem, and graph the feasible region. Let t be the number of tables
and c be the number of chairs.
10. A small publishing company is planning to publish 2 books this month: book A and book B. The publishing
cost is $6 each for book A and $8 each for book B. The total cost can be no more than $7,200. The company
cannot publish more than 560 copies of book A and 720 copies of book B. The profit per book A is $10, and
the profit per book B is $15. Find the number of books of each type that the company should publish to
maximize its profits.
Name: _______________________________
Review -- Linear Systems
Answer Section
MULTIPLE CHOICE
1. ANS: A
2. ANS: C
3. ANS: D
4. ANS: C
SHORT ANSWER
1. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
–2
–3
–4
–5
The solution to the system is (2, 4).
2. ANS:
4 hours
3. ANS:
10 minutes; 150 gallons
4. ANS:
(2, 3)
5. ANS:
(8, 7)
6. ANS:
5
x
Period: _____
Name: _______________________________
Period: _____
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
Graph
and
on the same coordinate plane. The solutions of the system are the
overlapping shaded regions, including the solid boundary line.
7. ANS:
y
72
64
56
48
40
32
24
16
8
8
16
24
32
40
48
56
64
72
80 x
8. ANS:
y
4
3
2
1
–4
–3
–2
–1
1
2
3
–1
–2
–3
–4
The shaded region is a rectangle.
4
x
Name: _______________________________
Period: _____
9. ANS:
c
72
64
56
48
40
32
24
16
8
8
16
24
32
40
48
56
64
72
80
t
10. ANS:
y
1200
900
(240, 720)
(0, 720)
600
(560, 480)
300
(560, 0)
(0, 0)
300
600
900
1200
x
The objective function is maximized at (240, 720), so the company should publish 240 copies of book A and
720 copies of book B.
PTS: 1
DIF: Average
REF: Page 207
NAT: 12.5.4.d
TOP: 3-4 Linear Programming
11. ANS:
Darnell’s Services yielded 3 dollars per dollar invested.
Stochy’s yielded 5 dollars per dollar invested.
Kammy’s Clothing yielded 7 dollars per dollar invested.
OBJ: 3-4.3 Problem-Solving Application
KEY: linear programming