140
CHAPTER 5, FORM F
COLLEGE ALGEBRA
NAME
DATE
Choose the best answer.
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.
2 – 3 1
4 2 6
xy
xy
=
=+
1. _____________
a. {(5, 3)}
b.
31
,
2
yy
ìü
æö
ïï
+
ïï
÷
ç÷
íý
ç÷
ç
ïï
èø
ïï
îþ
; infinitely many solutions
c.
Æ
; inconsistent
d. {(– 4, –3)}
2.
31
– –18
23
32–9
49
xy
xy
=
+=
2. ____________
a. {(12, 0)} b. {(0, 12)}
c. {(– 12, 0)} d.
Æ
; inconsistent
3.
3. ____________
a. {(–1, 2, – 4)} b. {(–2, 1, –1)}
c. {(1, –7, 2)} d. {(0, 3, –2)}
Use the Gauss-Jordan method to solve each system. Give the x-value of the
solution only.
4.
–5
2 3 5
xy
xy
=
+=
4. ____________
a. 4 b. 3 c. 2 d. –1
5.
– –2
2 – 11
3 – 6
x y z
xy
yz
+=
=
+=
5. ____________
a. 3 b. 2 c. 5 d. 4
141
CHAPTER 5, FORM F
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.
a.
2
.5 – – 3y x x=
b.
2–1.5 – 3y x x=
c.
2
.5 –1.5 3y x x=+
d.
2
.5 –1.5 – 3y x x=
Evaluate each determinant.
7.
9 10
–11 8
7. ____________
a.
−
182 b. 182 c. 99 d. –99
8.
–3 1 2
–5 6 0
–2 3 –1
8. ____________
a. 7 b. –27 c. –31 d.
23–
9. Use Cramer’s rule to find the x-value of the solution of the system 9. ____________
2 3 9
4 4 23.
xy
xy
– + = –
+=
a.
25
6
b.
23
8
c.
21
4
d.
1
2
10. Use Cramer’s rule to find the solution of the system 10. ____________
2 – 2 3
2
23
x y z
x y z
x y z
+=
– + =
+ + =
a. {(– 2, – 1, 3)} b. {(3, 4, 3)}
c. {(2, 1, 3)} d. {(1, 3, 4)}
CHAPTER 5, FORM F
142
11. Find the partial fraction decomposition of
2
32
2 – 3 3
–3
xx
x x x
+
+
. 11. _____________
a.
1 3 1
4( 1) 4( – 3)x x x
++
+
b.
1 –3 –1
4( 1) 4( – 3)x x x
++
+
c.
2
12
–3
x
xxx
+
++
d.
2
1 – 2
–3
x
xxx
++
Solve each nonlinear system of equations.
12.
22
30
8
xy
xy
+=
+=
12. ____________
a. {(4 + 2i, 4 – 2i), (4 – 2i, 4 + 2i)} b. {(5, 3)}
c. {(4 + i, 4 – i), (4 – i, 4 + i)} d.
Æ
13.
22
22
85
– 13
xy
xy
+=
=
13. ____________
a. {(7, – 6), (7, 6)} b. {(7, 6), (6, 7), (–7, – 6), (– 6, –7)}
c. {(– 7, – 6), (– 6, – 7)} d. {(7, 6), (– 7, 6), (7, – 6), (–7, – 6)}
14. A nonlinear system of two equations contains one equation whose 14. ____________
graph is a parabola and another equation whose graph is a circle.
What is the greatest possible number of points of intersection for
these two graphs?
a. 6 b. 1 c. 4 d. 2
15. Find two numbers such that their sum is 5 and the difference of their squares. 15.____________
is 105.
a. – 8 and 13 b. – 3 and 8 c. – 34 and 39 d. – 25 and 30
CHAPTER 5, FORM F
143
16. Graph the solution set of 16. ____________
2
4
–1 3.
yx
x
³
££
a.
b.
c.
d.
17. Use linear programming to solve the problem. 17. ____________
A company produces plastic cups and plates, both of which require time
on two machines, A and B. Manufacturing a unit of cups requires 2 hr
on machine A and 3 hr on machine B. Manufacturing a unit of plates
requires 2 hr on machine A and 1 hr on machine B. Each machine is
operated at most 12 hr per day.
If 1 unit of cups produces $50 profit per day and 1 unit of plates produces
$40 profit per day, find the number of units of cups and plates that will
produce maximum profit each day.
a. 3 units of cups and b. no units of cups and
3 units of plates 6 units of plates
c. 4 units of cups and d. 4 units of cups and
6 units of plates no units of plates
144
CHAPTER 5, FORM F
18. Find x in the equation
1 2 3 3 4 4 .
3 1 6 4 3 3
xy
xy
é ù é ù é ù
–
ê ú ê ú ê ú
+=
ê ú ê ú ê ú
– – –
ë û ë û ë û
18. ____________
a. x = –7 b. x = 6
c. x = 5 d. x = 3
Perform each operation, whenever possible, and give the entry in the first
row and first column of the result.
19.
79 2 3 0
4 0 3 1 4 6
62
éù
êú
éù
–
êú
êú
+
êú
êú
–
ëû
êú
ëû
19. ____________
a. –7 b. –7 c. 23 d. not possible
20.
1 4 5 3 9 1
22 5 9 6 2 4
é ù é ù
—
ê ú ê ú
+
ê ú ê ú
–
ë û ë û
20. ____________
a. 3 b. 5 c. 6 d. not possible
Write the second row of each matrix product, if the product can be found.
21.
31
23
24
46
50
éù
êú
éù
êú
êú
êú
êú
ëû
êú
ëû
21. ____________
a.
86
b.
59–
c.
20 30
d. product cannot be found
22.
32
31
54
65
21
éù
–
êú
éù
êú
êú
êú
êú
–
ëû
êú
ëû
22. ____________
a.
72–
b.
76
c.
92
d. product cannot be found
23. If A is a 1
´
3 matrix and B is a 3
´
1 matrix, find the size of the product 23. ____________
AB and the product BA, if these products can be found.
a. AB is 1
´
1; BA is 3
´
3
b. AB is 1
´
3; BA is 3
´
1
c. AB is 3
´
1; BA is 1
´
3
d. AB cannot be found; BA cannot be found
145
CHAPTER 5, FORM F
Find the entry in the first row and first column of each inverse, if the inverse exists.
24.
61
–3 2
éù
êú
êú
ëû
24. ____________
a.
1
6
b. – 6
c.
2
15
d. inverse does not exist
25.
34
9 12
éù
—
êú
êú
ëû
25. ____________
a. 3 b.
1
3
c.
1
–3
d. inverse does not exist
26.
1 –3 1
2 –2 1
3 1 0
éù
êú
êú
êú
êú
ëû
26. ____________
a. inverse does not exist b.
1−
c.
1
2
d.
3
2
−
27. Use the matrix inverse method to solve the system 27. ____________
4 – 5 11
27
2 1.
xy
xz
yz
=
+=
+=
Give the z-value of the solution only.
a. 1 b. 4 c. –1 d. –2
146
CHAPTER 5, FORM F