134
CHAPTER 5, FORM E
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 14
2 2 10
xy
xy
+=
+=
1. ____________
a. {(–3, 4)} b. {(–4, 9)}
c. {(4, 8)} d.
Æ
; inconsistent
2.
754
34
52 21
6
xy
xy
+=
-=
2. ____________
a. {(–6, 8)} b. {(6, 8)}
c. {(–6, –8)} d. {(6, –8)}
3.
2 – 3 – 2
– 4 2
– 3 1
x y z
x y z
x y z
=
+=
+=
3. ____________
a. {(–2, –3, –2)} b. {(1, 2, 9)}
c. {(–1, –1, –1)} d. {(2, 3, –7)}
Use the Gauss-Jordan method to solve each system. Give the x-value of the
solution only.
4.
5 – 28
4 2 28
xy
xy
=
+=
4. ____________
a. 6 b. 4 c. – 4 d. 2
5.
5. ____________
a. –1 b. 4 c.
2–
d. 1
CHAPTER 5, FORM E
135
6. Find the equation that defines the parabola shown on the screen, using 6. ____________
the information given at the bottom of the screen and in the table.
a.
2– .5 – 3y x x=
b.
2
2 – – 2y x x=
c.
2
2 – .5 – 3y x x=
d.
2–2y x x=+
Evaluate each determinant.
7.
–7 3
4 11
–
7. ____________
a. –89 b. 89 c. 56 d. –56
8.
7 9 7
029
006
–
–
8. ____________
a. –165 b. –84 c. 84 d. 165
9. Use Cramer’s rule to find the y-value of the 9. ____________
solution to the system
2 3 9
4 4 25
xy
xy
– + =
+=
.
a.
11
17
b.
3
5
c.
39
20
d.
43
10
10. Use Cramer’s rule to find the x-value of the 10.____________
solution of the system
3 6 43
7 5 53
9 27
x y z
x y z
x y z
– – = –
+ – =
+ + =
.
a. 2 b. 3 c. 6 d. 8
136
CHAPTER 5, FORM E
11. Find the partial fraction decomposition of
2
32
4 – 3 8
–4
xx
x x x
+
+
. 11. ____________
a.
2
2 2 –1
–4
x
xxx
++
b.
2
1 –2 2
4xx
x
++
+
c.
2
2 –2 1
–4
x
xxx
+
++
d.
2
2 –1 1
–2 ( – 2)
xx x
++
Solve each nonlinear system of equations.
12.
12
2 – 5
xy
xy
=
=
12. ____________
a. {(4, 3)} b.
3
(4, 3), , – 8
2
ìü
æö
ïï
ïï
÷
ç–÷
íý
ç÷
ç
ïï
èø
ïï
îþ
c. {(4, 3), (–4, –3)} d.
Æ
13.
22
39
3
xy
xy
-=
-=
13. ____________
a. {(– 8, – 5)} b. {(8, – 5)}
c. {(– 8, 5)} d. {(8, 5)}
14. A nonlinear system of two equations contains one equation whose graph is a 14. ____________
circle and another equation whose graph is a line. What is the greatest possible
number of points of intersection for these two graphs?
a. 1 b. 2 c. 3 d. 4
15. Find two numbers such that their sum is 1 and the sum of their squares is 145. 15. ____________
a. 9 and – 8 b. 9 and 8 c. 81 and 64 d. 81 and – 64
CHAPTER 5, FORM E
137
16. Graph the solution set of
22
9
2 – 2.
xy
xy
+<
>
16. ____________
a.
b.
c.
d.
17. Use linear programming to solve the problem. 17. ____________
A company produces widgets and gadgets, both of which
require time on two machines, A and B. Manufacturing 100
widgets requires 1 hr on machine A and 2 hr on machine B.
Manufacturing 100 gadgets requires 3 hr on machine A and 2 hr
on machine B. Each machine is operated at most 18 hr per day.
If 100 widgets produce $30 profit and 100 gadgets produce $20
profit, how many widgets and gadgets will produce a maximum
profit each day?
a. 450 widgets and 450 gadgets
b. No widgets and 600 gadgets
c. 900 widgets and no gadgets
d. 900 widgets and 600 gadgets
CHAPTER 5, FORM E
138
18. Find x in the equation
3 4 3 9
2 4 2 4
xx
é ù é ù
–
ê ú ê ú
=
ê ú ê ú
—
ë û ë û
. 18. ____________
a. 3 b. 0 c. 2 d.
3–
Perform each operation, whenever possible, and give the entry in the first row and
first column of the result.
19.
– 6 5 72
4 0 1 81
2 –3
éù
êú
éù
êú
êú
+
êú
êú
ëû
êú
ëû
19. ____________
a. –31 b. –24
c. not possible d. 16
20.
– 6 2 8 –3
1
–
0 4 7 –5
2
é ù é ù
ê ú ê ú
ê ú ê ú
ë û ë û
20. ____________
a. –2 b. –8
c. not possible d. –10
Write the second row of each matrix product, if the product can be found.
21.
21
2 –1
4 –2 05
3 –3
éù
êú
éù
êú
êú
êú
êú
ëû
êú
ëû
21. ____________
a.
43
b.
6 –18
c.
8 –14
d. product cannot be found
22.
[ ]
3 –1 1
–2 7 –1 4 0 –6
éù
êú
êú
ëû
22. ____________
a.
73–
b.
3 –12
c.
12 15–
d. product cannot be found
23. If A is a 2
´
1 matrix and B is a 1
´
1 matrix, find the size of the 23. ____________
product AB and the product BA, if these products can be found.
a. AB is 1
´
2; BA is 1
´
1
b. AB is 2
´
2; BA is 1
´
1
c. AB cannot be found; BA is 1
´
2
d. AB is 2
´
1; BA cannot be found
CHAPTER 5, FORM E
139
Find the entry in the first row and first column of each inverse, if the inverse exists.
24.
31
1 –3
éù
êú
êú
ëû
24. ____________
a.
3
10
b.
1
10
c.
3
–10
d. inverse does not exist
25.
–2 6
3 –9
éù
êú
êú
ëû
25. ____________
a. inverse does not exist b.
1
3
c.
1
6
d.
1
9
–
26.
1 1 –2
1 0 1
1 2 –2
éù
êú
êú
êú
êú
ëû
26. ____________
a.
1
2
−
b. inverse does not exist
c.
2
3
d. –1
27. Use the matrix inverse method to solve the system 27. ____________
2 3 3
3 – 4 1
20
xy
xz
yz
+=
=
+=
.
Give the z-value of the solution only.
a. 3 b. –1 c. –3 d. 2
140
CHAPTER 5, FORM E