MTH: 160 COLLEGE ALGEBRA
CHAPTER 6 Review
NAME_________________________
Please show all your work on this test
and place your final answers in the provided spaces.
Thank you and good luck.
1) (19 PTS) Solve systems by methods described. If any solutions are infinitely many
give the generic solution.
a) Solve the system graphically.
Ans:__________________
Use calculator and show graph.
2x  y  2
4 x  3 y  24
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b) Solve by substitution method.
Ans:__________________
4x  y  2
2 y  8 x  4
c) Solve by elimination method.
Ans:_______________________
2x  6y  7
1
10
xy 
3
9
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2) (15 PTS) Given
m  2n  t  1
2m
 t 1
m n
 1
Solve the system using Gauss elimination and backwards substitution. Please
provide the matrix solution from your grapher. Rewrite the matrix solution with
coefficients and variables before doing backwards substitution. Convert all answers to
improper fractions.
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Solve the system using Gauss-Jordan Elimination (rref). Please provide the matrix
solution from your grapher.
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3) (6 PTS) Given the matrix equation, AX  B, solve for X. Please show all supporting steps!
4) (9 PTS) Given
3 x  3 y  2z  4
x  3 y  z  10
5 x  2y  3z  8
a) Write an equivalent matrix equation AX  B.
b) Use a grapher to solve the system.
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X 
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5) (5 PTS) Given
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
 x
 8
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 3
21
2y  1
6
2 
3

5  =  8
 3
z  7 
21
9
6
2
5  , Find x, y & z
12 
Ans:___________________________
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6) (24 PTS) Matrix Operations
 9 0
 4 6 
a) Given A  
and B  

 , Find A  B
-3 6 
7 8 
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4 8 
 3 1 5
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b) Given A  
 and B   1 1  , Find AB
-2
0
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
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0 3 
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 1 1
7) (10 pts) Given A   2 3
 1 1
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
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2
1  'evaluate the determinant
3 
A
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using the "Hot Dog" method.
Ans:_____________________________
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8) A 3-oz serving of roasted, skinless chicken breast contains 140 Cal, 27 g of protein, 3 g
of fat, 13 mg of calcium, and 64 mg of sodium. One-half cup of potato salad contains
180 Cal, 4 g of protein, 11 g of fat, 24 mg of calcium, and 662 mg of sodium. One
broccoli spear contains 50 Cal, 5 g of protein, 1 g of fat, 82 mg of calcium, and 20 mg
of sodium.
a)
Write 1 X 5 matrices C, P, and B that represent the nutritional values of each
food.
b)
Find C + 2P + 3B and tell what the entries represent.
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9) Analyze the different solutions you can get when solving a 3 X 3 matrix on the
grapher. Please write your matrix before and after solving. State whether the results
from the grapher denote one solution, no solution or infinitely many solutions and the
reason for you conclusion.
mnt 9
m  n  t  15
3m  n  t  2
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2 x  3 y  2z  2
x  4y  z  9
3 x  y  5z  5
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p  q  r 1
p  2q  3r  4
4 p  5q  6r  7
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10)
The total volume of passenger traffic by private automobile, by bus (excluding school
buses and urban transit buses), and by railroads in the United States in a recent
year was 1899 billion passenger-miles. (One passenger-mile is the transportation of
one passenger the distance of one mile.) The volume of bus traffic was 21 billion
passenger-miles more than the volume of railroad traffic. The total volume of bus
traffic was 1815 billion passenger-miles less than the volume of traffic by private
automobile. What was the volume of each type of passenger traffic?
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