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
solve the following system of equations .
![## System of Linear Equations
In this activity, we will analyze a system of linear equations and identify the correct solution set.
### Given Equations
1. \( x - 3y + 6z = 8 \)
2. \( 3x - 9y + 18z = 24 \)
### Solution Set Options
Consider the following solution set options and select the correct one.
1. \( \varnothing \) (the null set)
2. \( \{\{2y + 5, y, 3y + 10\}\} \)
3. \( \{\{x, 3x - 1, 2x\}\} \)
4. \( \{(x, y, z)| x - 3y + 6z = 8 \}\)
### Explanation:
- Option 1 (\( \varnothing \)): Indicates that there are no solutions.
- Option 2 (\( \{\{2y + 5, y, 3y + 10\}\} \)): Represents a parametric solution where \( y \) is the free variable.
- Option 3 (\( \{\{x, 3x - 1, 2x\}\} \)): Also represents a parametric solution where \( x \) is the free variable.
- Option 4 (\( \{(x, y, z)| x - 3y + 6z = 8 \}\)): Defines the solution set as consistent with the first equation.
### Instruction:
Please analyze the given system of equations and use your understanding of linear algebra to determine the correct solution.
---
Posted temperature: 87°F, partly sunny.
For any further explanations or queries, feel free to reach out.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff19158ce-506a-4a94-9506-84274a4b7439%2F90ce13bd-59c5-4680-9788-e462e3a782f3%2F7kuq2fj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## System of Linear Equations
In this activity, we will analyze a system of linear equations and identify the correct solution set.
### Given Equations
1. \( x - 3y + 6z = 8 \)
2. \( 3x - 9y + 18z = 24 \)
### Solution Set Options
Consider the following solution set options and select the correct one.
1. \( \varnothing \) (the null set)
2. \( \{\{2y + 5, y, 3y + 10\}\} \)
3. \( \{\{x, 3x - 1, 2x\}\} \)
4. \( \{(x, y, z)| x - 3y + 6z = 8 \}\)
### Explanation:
- Option 1 (\( \varnothing \)): Indicates that there are no solutions.
- Option 2 (\( \{\{2y + 5, y, 3y + 10\}\} \)): Represents a parametric solution where \( y \) is the free variable.
- Option 3 (\( \{\{x, 3x - 1, 2x\}\} \)): Also represents a parametric solution where \( x \) is the free variable.
- Option 4 (\( \{(x, y, z)| x - 3y + 6z = 8 \}\)): Defines the solution set as consistent with the first equation.
### Instruction:
Please analyze the given system of equations and use your understanding of linear algebra to determine the correct solution.
---
Posted temperature: 87°F, partly sunny.
For any further explanations or queries, feel free to reach out.
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