Name ______________________________
Class __________ Date __________
Algebra 2 – Chapter 3 Test
1.
Classify the system
x  5   y

2 y  10  2 x
as independent, dependent, or inconsistent without graphing.
Solve each system.
2.
5.
 y  2x  8

 y  3x  1
3.
3 x  y  2

2 x  2 y  4
4.
y  x  2

2 x  y  1
Fix-It-Fast Plumbing charges $25 for a house call and $50 for each hour spent on the job. Do-It-Right Plumbing charges $35
for a house call and $45 for each hour spend on the job. How many hours must be spent on the job in order for the charges of
the two plumbing companies to be equal?
Graph each system.
6.
y  x  5

3 x  y  2
7.
y  x  2

 y | x  3 | 1
8
8
6
6
4
4
2
2
-8 -7 -6 -5 -4 -3 -2 -1
1 2 3 4 5 6 7 8
-8 -7 -6 -5 -4 -3 -2 -1
-2
-2
-4
-4
-6
-6
-8
-8
1 2 3 4 5 6 7 8
Name ______________________________
Class __________ Date __________
Graph each system of constraints. Find all vertices. Evaluate the objective function at each vertex to find the maximum and
minimum value.
x  3

8.  y  7
 x  0, y  0

2 x  y  30

9.  x  y  20
 x  0, y  0

Maximum for P  2 x  3 y
Use a Scale of 5
Minimum for C  x  4 y
Not (0, 0)
Vertices: _______________________________________
Vertices: ____________________________________
Maximum: __________________
Minimum: _________________
10a. Jerome walks between 10 and 20 min each day and runs between 30 and 45 min each day. He never spends more than 60
minutes running and walking together. Write the equations, graph, and find all vertices.
Use a Scale of 10
10b.
Jerome burns 4 cal/min walking and 10 cal/min running, How much time should be spent on each activity to maximize
the number of calories he burns?
Name ______________________________
Class __________ Date __________
Graph and label each point.
11.
A (0, 4, 0)
12.
B (-4, 0, 0)
13.
C (2, 0, 5)
14.
D (3, 0, -2)
15.
E (4, 1, -1)
16.
F (3, -3, 1)
Graph each equation.
17. x  2 y  z  4
19.  x  2 y  z  4
18. 6 x  2 y  3z  12
Name ______________________________
Class __________ Date __________
Solve each system of equations.
20.
5 x  4 y  z  1

2 x  2 y  z  1
 x  y  z  2

21.
x  2 y  0

4 x  z  4
5 y  z  1

Solve.
22. Jennifer has ten fewer quarters than dimes and five fewer nickels than quarters. The total value of the coins is $4.75. How
many quarters, nickels, and dimes does she have?
Given:
q = d – 10, q = n + 5, d = n + 15
.25q + .1d + .05n = $4.75
23. Which point gives the minimum value for P = 3x + 2y and lies within the system of restrictions?
1  x  6

2  y  5
 x  y  10

A.
(1, 2)
B.
(0, 0)
C.
(5, 5)
D.
(1, 5)
Extra Credit.
Hemlock Stones, the not yet famous consulting detective, has just been called in to solve the mysterious
murder at the Socratic Liar’s Club. There are five suspects each of whom has sworn by the club oath to
make two true statements and one false one whenever speaking to someone on the club’s premises.
From their recorded statements below, Hemlock Stones was able to determine “who dunit.” Can you?
Professor: I did not kill Henley. I never owned a knife. Lance did it.
Ethel: I didn’t kill him. I don’t own a knife. The others are crazy.
Phoebe: I’m innocent. Lance is the killer. I don’t even know Dutch.
Lance: I’m innocent. Dutch is guilty. The Professor lied when he said I did it.
Dutch: I didn’t kill him. Ethel is the murderer. Phoebe and I are old friends.
Who is the murderer? ___________________________