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(1) x-3y+6z= 8 (2) 3x-9y+18z = 24

(1) x-3y+6z= 8 (2) 3x-9y+18z = 24

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 3GP
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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.
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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