CHAPTER 5, FORM B
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.
– 3 4
2 6 2
xy
xy
=
– + =
1. _______________________________
2.
2–2
317
2
xy
xy
=
+=
2. _______________________________
3.
3 2 1
2 – 3 4
4 5 2
x y z
x y z
x y z
+ – = –
+=
+ – = –
3. _______________________________
Use the Gauss-Jordan method to solve each system.
4.
4 3 1
–3 – 5 –20
ab
ab
+=
=
4. _______________________________
5.
2 4 –10 –2
3 9 21 0
5 12 1
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.
44
15
–
–
7. _______________________________
8.
2 3 5
4 1 3
3 2 1
–
–
–
8. _______________________________
CHAPTER 5, FORM B
Solve each system by Cramer’s rule.
9.
2 2 1
4 3 –5
xy
xy
+=
-=
9. _______________________________
10.
3
26
2 2 3
x y z
x y z
x y z
– + =
+ + =
– + =
10. _______________________________
11. Find the partial fraction decomposition of 11. _______________________________
2
2
2 7 9.
21
xx
xx
++
++
Solve each nonlinear system of equations.
12.
2
1
– –1
xy
xy
+=
=
12. _______________________________
13.
22
22
33
–1
xy
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 circle, can the system have exactly one
solution? If so, draw a sketch to indicate this situation.
15. Find two numbers such that their sum is 15 and the difference 15. _______________________________
of their squares is 15.
16.
Graph the solution set of
2 – 3 6
5 5.
xy
xy
³
+³
16.
CHAPTER 5, FORM B
17.
Use linear programming to solve the problem.
The Acme Glass 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. _______________________________
5 7 5 10 .
2 4 2 3
x
y z y z
é ù é ù
–
ê ú ê ú
=
ê ú ê ú
++
ë û ë û
Perform each operation, whenever possible.
19.
3 2 5 2
1 3 2 0
4 2 1 4
é ùé ù
ê úê ú
ê úê ú
ê úê ú
ê úê ú
ë ûë û
19. _______________________________
20.
2 0 1 –3 8 –3
–4
– 6 5 7 –2 –5 4
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.
45
2 4 8 60
–7 9 –5 43
éù
–
êú
éù
êú
êú
+êú
êú
ëû
êú
–
ëû
21. _______________________________
22. If A is a 3
´
4 matrix and B is a 5
´
3 matrix, find the size 22. _______________________________
of the product AB and the product BA, if these products
can be found.
Find the inverse, if it exists, of each matrix.
23.
3 –2
12 –8
éù
êú
êú
ëû
23. _______________________________
CHAPTER 5, FORM B
24.
1 2 0
0 4 2
112
éù
êú
êú
êú
êú
—
ëû
24. _______________________________
25. Use the matrix inverse method to solve the system 25. _______________________________
37
2 – 5 –1.
xy
xy
+=
=
CHAPTER 5, FORM B
