Name ______________________________
Class __________ Date __________
Algebra 2 – Chapter 3 Test
1.
Classify the system
x  5   y

2 y  10  2 x
without graphing (SHOW ALL WORK!!!).
(Ind/Dep/Inconsist)
__________________
Solve each system. SHOW ALL WORK!!!
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? Write equation(s) and solve algebraically. SHOW ALL WORK!!!
Graph each system. SHOW ALL WORK!!!
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 or
minimum value. SHOW ALL WORK!!!
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
OTHER THAN (0, 0)
Vertices: _______________________________________
Vertices: ____________________________________
Maximum: __________________
Minimum – other than (0, 0): _________________
10a. Jerome walks from 10 and 20 minutes each day and runs from 25 and 35 minutes each day. He never spends more than 50
minutes walking and running together. Define your variables, write the inequalities, graph, and find all vertices.
USE A SCALE OF 5 ON YOUR GRAPH
10b. Jerome burns 4 cal/min walking and 10 cal/min running. Write the objective function for this problem. How much time
should be spent on each activity to maximize the number of calories he burns? SHOW ALL WORK!!!
Name ______________________________
Class __________ Date __________
Solve each system of equations. SHOW ALL WORK ON THE LINES PROVIDED!!!
11.
5 x  4 y  z  1

2 x  2 y  z  1
 x  y  z  2

12.
x  2 y  1

x  3 y  z  0
z  x  9

Solve.
13. 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? (q=quarters, d=dimes, n=nickels) SOLVE USING ALGEBRAIC
TECHNIQUES FOR SOLVING THREE-VARIABLE SYSTEMS. SHOW ALL WORK ON THE LINES
PROVIDED!!!
Given: q = d – 10
q–5=n
.25q + .1d + .05n = 4.75
Extra Credit. SHOW WORK ON BACK PAGE!!!
Monica has $1, $5, and $10 bills in her wallet that are worth $96. If she had one more $1 bill, she would have just as
many $1 bills as $5 and $10 bills combined. She has 23 bills total. How many of each denomination (type of bill) does she have?