CHAPTER 5, FORM A
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.
21
2 3 12
xy
xy
+ = –
-=
1. _______________________________
2.
32
–1
43
343
23
xy
xy
=
– + =
2. _______________________________
3.
2 –1
2 – 9
3 3 6
x y z
x y z
x y z
+ – =
+=
+ + =
3. _______________________________
Use the Gauss-Jordan method to solve each system.
4.
10 – 3 5
5 2 –8
mn
mn
=
+=
4. _______________________________
5.
2 –2
21
– 2 – 3
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.
52
65–
7. _______________________________
8.
3 1 –2
4 2 5
6 3 1—
8. _______________________________
CHAPTER 5, FORM A
Solve each system by Cramer’s rule.
9.
4 2 2
36
xy
xy
+ = –
-=
9. _______________________________
10.
2 2 3
2
23
x y z
x y z
x y z
– + =
– + =
+ + =
10. _______________________________
11. Find the partial fraction decomposition of 11. _______________________________
2
32
4 – 5 15 .
– 4 5
xx
x x x
–
–
Solve each nonlinear system of equations.
12.
22
22
–4
6
xy
xy
=
+=
12. _______________________________
13.
3 12
9
xy
xy
+=
=
13. _______________________________
14. If a system of two nonlinear equations contains one equation 14. _______________________________
whose graph is a circle and another equation whose graph is a
parabola, 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 72 and their 15. _______________________________
difference is 38.
16.
Graph the solution set of
2 – 3 6
–0
04
0.
xy
xy
x
y
£
³
££
³
16.
CHAPTER 5, FORM A
17.
Use linear programming to solve the problem.
A company produces two models of lamps, A and B. They can
produce up to 1500 lamps each day using a total of 60 hr of
labor. It takes 3 min of labor to make one model A lamp and
2 min of labor to make one model B lamp. Graph the
feasibility
region and label the vertices.
How many of each model should be made daily in order to
maximize the company’s profit if the profit on a
model A lamp is $4 and the profit on a model B lamp is $3?
17.
_______________________________
18. Find the value of each variable in the equation 18. _______________________________
[ ] [ ]
3 5 2 4 2 5 2 .x y z x z– + – = +
Perform each operation, whenever possible.
19.
2 1 3 1 2 3
1 2 –1 2 – 2 1
0 1 0 0 0 1
é ùé ù
ê úê ú
ê úê ú
ê úê ú
ê úê ú
ë ûë û
19. _______________________________
20.
1 –8 10 –1 9 12 0 2 –1
5 2 –3 8 6 7 5 6 3
– 4 0 0 –3 4 5 –7 11 2
é ù é ù é ù
ê ú ê ú ê ú
ê ú ê ú ê ú
++
ê ú ê ú ê ú
ê ú ê ú ê ú
ë û ë û ë û
20. _______________________________
21.
3 1 2 1 2 2
53
4 3 2 5 5 3
é ù é ù
—
ê ú ê ú
+
ê ú ê ú
– – – –
ë û ë û
21. _______________________________
22. If A is a 4
´
1 matrix and B is a 1
´
4 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.
2 – 4
47
éù
êú
êú
–
ëû
23. _______________________________
CHAPTER 5, FORM A
24.
1 1 0
0 0 3
0 2 1
éù
êú
êú
êú
êú
ëû
24. _______________________________
25. Use the matrix inverse method to solve the system 25. _______________________________
4 – 3 –14
6 5 17.
xy
xy
=
+=
CHAPTER 5, FORM A
