Answers to Chapter Test Forms
1
CHAPTER 5, FORM D
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.
4 5 13
34
xy
xy
+=
+ = –
1. _______________________________
2.
1 1 1
2 3 6
1 1 1
4 3 12
xy
xy
+=
– = –
2. _______________________________
3.
2 – – 8
2 – 3 – 4 6
–0
x y z
x y z
x y z
=
=
+=
3. _______________________________
Use the Gauss-Jordan method to solve each system.
4.
4 8 20
3 –7
rs
rs
-=
– + =
4. _______________________________
5.
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 –10
35
7. _______________________________
8.
0 4 3
2 –0 4
5 1 0
–
–
8. _______________________________
Answers to Chapter Test Forms
2
CHAPTER 5, FORM D
Solve each system by Cramer’s rule.
9.
3 4 5
7 8 11
xy
xy
+ = –
– + =
9. _______________________________
10.
2 3 1
26
3 2 13
x y z
x y z
x y z
– – = –
+ + =
+ – =
10. _______________________________
11. Find the partial fraction decomposition of 11. _______________________________
2
3
9 3 8.
2
xx
xx
-+
+
Solve each nonlinear system of equations.
12.
22
22
2 3 6
3 2 35
xy
xy
-=
+=
12. _______________________________
13.
22
44
2 – 0
xy
xy
+=
=
13. _______________________________
14. If a nonlinear system of two equations contains one equation 14. _______________________________
whose graph is a line and another equation whose graph is a
parabola, 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 2 and the sum of their 15. _______________________________
squares is 52.
16.
Graph the solution set of
2
0
2.
xy
x
yx
£
£
£+
16.
Answers to Chapter Test Forms
3
CHAPTER 5, FORM D
17.
Use linear programming to solve the problem.
A company produces two types of desks, kneehole
and rolltop. They can produce up to 25 desks each
week using a total of 300 hr of labor. It takes 10 hr of
labor to produce a kneehole desk and 15 hr of labor to
produce a rolltop desk. Graph the feasibility region and
label the vertices.
How many desks of each type should be made weekly
to maximize the company’s profit if the profit on a
kneehole desk is $15 and the profit on a rolltop desk is $20?
17.
_______________________________
18. Find a, b, c, and d so that 18. _______________________________
1 4 1 0
0 1 0 1
ab
cd
é ùé ù é ù
ê úê ú ê ú
=
ê úê ú ê ú
ë ûë û ë û
Perform each operation, whenever possible.
19.
1 –3 2 3 2 1
4 0 5 0 –1 6
– 6 1 –2 5 4 1
é ùé ù
ê úê ú
ê úê ú
ê úê ú
ê úê ú
ë ûë û
19. _______________________________
20.
1 2 4
3 2 0 0 2 3
1 4 6 5 0 3
éù
–
êú
éù
êú
êú
–
êú
êú
—
ëû
êú
ëû
20. _______________________________
21.
3 1 1 4
2 4 3 6
20 3 3 7
2 8 3 2
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
–
ê ú ê ú
ë û ë û
21. _______________________________
22. If A is a 3
´
2 matrix and B is a 2
´
4 matrix, find the 22. _______________________________
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.
39
26
éù
êú
êú
ëû
23. _______________________________
Answers to Chapter Test Forms
4
CHAPTER 5, FORM D
24.
1 –1 1
1 2 0
2 2 1
éù
êú
êú
êú
êú
ëû
24. _______________________________
25. Use the matrix inverse method to solve the system 25. _______________________________
2 – 4 3
3 1.
xy
xy
=
+=
Answers to Chapter Test Forms
5
CHAPTER 5, FORM D