Answers to Chapter Test Forms 1
CHAPTER 5, FORM C
COLLEGE ALGEBRA
NAME
DATE
Use substitution or elimination to solve each system. Identify any
system that is inconsistent or has infinitely many solutions. If a system
has dependent equations, express the solution with y arbitrary.
1.
28
3 2 2
xy
yx
-=
= – +
1. _______________________________
2.
137
421
xy
xy
+=
+=
2. _______________________________
3.
2 – –1
– 2 2 7
34
x y z
x y z
x y z
+=
+=
+ + =
3. _______________________________
Use the Gauss-Jordan method to solve each system.
4.
3 2 4
– 6 5 19
rs
rs
+=
+=
4. _______________________________
5.
2 4 4
4 – 8 7 2
2 4 3 5
x y z
x y z
x y z
– + = –
+=
– + – =
5. _______________________________
6. Find the equation that defines the parabola shown on 6. _______________________________
the screen, using the information given at the bottom
of the screen and in the table.
Evaluate each determinant.
7.
7. _______________________________
8.
3 1 2
5 2 4
7 3 –6
–
—
8. _______________________________
Answers to Chapter Test Forms 2
CHAPTER 5, FORM C
Solve each system by Cramer’s rule.
9.
6 3 9
3 9 7
xy
xy
– – = –
+=
9. _______________________________
10.
24
2 3 3
5
x y z
x y z
x y z
+ + = –
+ + =
– + = –
10. _______________________________
11. Find the partial fraction decomposition of 11. _______________________________
2
32
19 50 25.
35
xx
xx
+-
–
Solve each nonlinear system of equations.
12.
22
– 2 2
2
xy
xy
=
=
12. _______________________________
13.
221
3
y x x
xy
= + +
+=
13. _______________________________
14. If a nonlinear system of two equations contains one 14. _______________________________
equation whose graph is a parabola and another equation
whose graph is a line, can the system have exactly two
solutions? If so, draw a sketch to indicate this situation.
15. Find two numbers such that their sum is
27
5
and their product 15. _______________________________
is 2.
16.
Graph the solution set of
2
22
3 – .
xy
yx
>+
<
16.
Answers to Chapter Test Forms 3
CHAPTER 5, FORM C
17.
Use linear programming to solve the problem.
The Acme Class Ring Company designs and sells two
types of rings: the VIP and the SST. They can produce
up to 24 rings each day using up to 60 total man-hours of
labor. It takes 3 man-hours to make one VIP ring, and 2
man-hours to make one SST ring. Graph the feasibility
region and label the vertices.
How many of each type of ring should be made daily in
order to maximize the company’s profit, if the profit on a
VIP ring is $40 and the profit on an SST ring is $35?
17.
_______________________________
18. Find the value of each variable in the equation 18. _______________________________
3 1 2 2
2 3 2 9
x x y
z
é ù é ù
+ – – –
ê ú ê ú
=
ê ú ê ú
ë û ë û
Perform each operation, whenever possible.
19.
23
0 4 3
4 –1 5 1 –2
05
éù
êú
éù
êú
êú
êú
êú
ëû
êú
ëû
19. _______________________________
20.
6 5 7 – 6
–3 4 2 8
é ù é ù é ù
ê ú ê ú ê ú
++
ê ú ê ú ê ú
ë û ë û ë û
20. _______________________________
21.
7 2 1 0
– 6 8 – 3 4 –2
5 –1 6 5
é ù é ù
ê ú ê ú
ê ú ê ú
ê ú ê ú
ê ú ê ú
ë û ë û
21. _______________________________
22. If A is a
25´
matrix and B is a
52´
matrix, find 22. _______________________________
the size of the product AB and the product BA, if
these products can be found.
Find the inverse, if it exists, of each matrix.
23.
23. _______________________________
Answers to Chapter Test Forms 4
CHAPTER 5, FORM C
24.
1 0 4
0 1 3
1 0 5
éù
êú
êú
–
êú
êú
ëû
24. _______________________________
25. You have 25 coins, all of which are quarters and dimes. 25. _______________________________
If the value of the coins is $3.25, how many of each type
of coin do you have?
Answers to Chapter Test Forms 5
CHAPTER 5, FORM C
126