Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Solving the System of Equations
Solve the following system of equations:
1. \( x - 5y + z = 12 \)
2. \( -y + 2z = 8 \)
3. \( z = 0 \)
Choose the correct solution from the following options:
- \( (-28, 8, 0) \)
- \( (-28, -8, 0) \)
- \( (52, 8, 0) \)
#### Explanation:
1. From equation (3), we know that \( z = 0 \).
2. Substitute \( z = 0 \) into equation (2):
\[
-y + 2(0) = 8 \implies -y = 8 \implies y = -8
\]
3. Substitute \( y = -8 \) and \( z = 0 \) into equation (1):
\[
x - 5(-8) + 0 = 12 \implies x + 40 = 12 \implies x = 12 - 40 \implies x = -28
\]
Thus, the solution to the system of equations is \( (x, y, z) = (-28, -8, 0) \).
This correct option is:
- \( (-28, -8, 0) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff19158ce-506a-4a94-9506-84274a4b7439%2F7d0095fe-5df6-45e4-b71b-2d10c06ca871%2Fx56hwc6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the System of Equations
Solve the following system of equations:
1. \( x - 5y + z = 12 \)
2. \( -y + 2z = 8 \)
3. \( z = 0 \)
Choose the correct solution from the following options:
- \( (-28, 8, 0) \)
- \( (-28, -8, 0) \)
- \( (52, 8, 0) \)
#### Explanation:
1. From equation (3), we know that \( z = 0 \).
2. Substitute \( z = 0 \) into equation (2):
\[
-y + 2(0) = 8 \implies -y = 8 \implies y = -8
\]
3. Substitute \( y = -8 \) and \( z = 0 \) into equation (1):
\[
x - 5(-8) + 0 = 12 \implies x + 40 = 12 \implies x = 12 - 40 \implies x = -28
\]
Thus, the solution to the system of equations is \( (x, y, z) = (-28, -8, 0) \).
This correct option is:
- \( (-28, -8, 0) \)
Transcribed Image Text:### Coordinate Selection Exercise
Please select the correct coordinate point from the options below:
- ☐ (-28, 8, 0)
- ☐ (-28, -8, 0)
- ☐ (52, 8, 0)
- ☐ (52, -8, 0)
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