AnswersTN-Algebra II B SC 26-27 For CreditPiecewise Defined Functions

Solving 3 x 3 Linear Systems Answers

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Several customers order small fruit baskets filled with apples, bananas, and oranges. Let a represent the price per pound of apples, b represent the price per pound of bananas, and c represent the price per pound of oranges. The system represents the number of pounds of each type of fruit and the total price of each fruit basket. How much per pound does each type of fruit cost?

Question illustration
A
apples: $2.00/lb, bananas: $0.50/lb, and oranges: $3.00
B
apples: $2.00, bananas: $1.50/lb, and oranges: $3.00/lb
C
apples: $2.50/lb, bananas $0.25/lb, and oranges: $3.00/lb
D
apples: $2.50, bananas: $0.75, oranges: 3.00/lb
2
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What is the solution to the following system?

Question illustration
A
x = 10, y = 2, z = 5
B
x = –4, y = 2, z = 5
C
x = 0, y = 2, z = 5
D
x = 4, y = 6, z = 5
3

The cost for three packages of moving boxes is modeled by the system of equations below. Let s represents the cost of each small box, m represents the cost of each medium box, and l represents the cost of each large box. Which ordered triple (s, m, l) represents the costs of the three boxes?

Question illustration
A
(1.00, 2.50, 3.50)
B
(1.00, 2.00, 2.90)
C
(1.50, 2.00, 2.75)
D
(1.50, 2.00, 2.00)
4

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

A
The system can be either inconsistent or consistent.
B
The system can be either independent or dependent.
C
The system can only be independent and consistent.
D
The system can only be dependent and inconsistent.
5

What is the solution to the following system?

Question illustration
A
(3, –1, 4)
B
(4, 1, 3)
C
(4, –1, 3)
D
(3, 1, 4)
6

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
7

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
8

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
9

What is the solution to the following system?

Question illustration
A
(8, 40, 32)
B
(10, 2, 3)
C
(20, 4, 5)
D
(40, 8, 10)
10

What is the solution to the following system?

Question illustration
A
(3, 1, 0)
B
(0, 1, 0)
C
(2, 1, 0)
D
(–2, 1, 0)
11

A system of three linear equations in three variables is consistent and independent. How many solutions to the system exist?

A
none
B
one
C
three
D
infinitely many
12

A system of three linear equations in three variables is inconsistent. How many solutions to the system exist?

A
none
B
one
C
three
D
infinitely many
13

What is the solution to the following system?

Question illustration
A
x = 0, y = 1, z = 2
B
x = 1, y = –1, z = 2
C
x = 1, y = 0, z = –1
D
x = 2, y = 1, z = 0
14

A system of three linear equations in three variables is consistent and dependent. How many solutions to the system exist?

A
none
B
one
C
three
D
infinitely many

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