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Solve the system of linear equations, if possible. State any solutions and classify each system as consistent independent, consistent dependent, or inconsistent. If not possible, enter DNE in part (b). If the system is dependent, enter x and y in terms of z. - 2x - 2y 2z = -6 - x - 3y + 2z = − 6 3x + y2z = - 2

Solve the system of linear equations, if possible. State any solutions and classify each system as consistent independent, consistent dependent, or inconsistent. If not possible, enter DNE in part (b). If the system is dependent, enter x and y in terms of z. - 2x - 2y 2z = -6 - x - 3y + 2z = − 6 3x + y2z = - 2

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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## Solving the System of Linear Equations ### Instructions Solve the system of linear equations, if possible. State any solutions and classify each system as consistent independent, consistent dependent, or inconsistent. If not possible, enter **DNE** in part (b). If the system is dependent, enter \( x \) and \( y \) in terms of \( z \). ### Given Equations \[ \begin{align*} -2x - 2y - 2z &= -6 \\ -x - 3y + 2z &= -6 \\ 3x + y - 2z &= -2 \\ \end{align*} \] ### Classification (a) The system of equations is: - ○ Inconsistent. - ○ Consistent dependent. - ○ Consistent independent. ### Solution (b) The solution to the system is: - \( x = \) [input box] - \( y = \) [input box] - \( z = \) [input box] ### Explanation When solving a system of equations, the classification and solution depend on the relationships between the equations: - **Inconsistent**: The equations have no solutions. - **Consistent dependent**: The equations are dependent on one another and have infinitely many solutions. - **Consistent independent**: The equations are independent and have a unique solution.
Transcribed Image Text:## Solving the System of Linear Equations ### Instructions Solve the system of linear equations, if possible. State any solutions and classify each system as consistent independent, consistent dependent, or inconsistent. If not possible, enter **DNE** in part (b). If the system is dependent, enter \( x \) and \( y \) in terms of \( z \). ### Given Equations \[ \begin{align*} -2x - 2y - 2z &= -6 \\ -x - 3y + 2z &= -6 \\ 3x + y - 2z &= -2 \\ \end{align*} \] ### Classification (a) The system of equations is: - ○ Inconsistent. - ○ Consistent dependent. - ○ Consistent independent. ### Solution (b) The solution to the system is: - \( x = \) [input box] - \( y = \) [input box] - \( z = \) [input box] ### Explanation When solving a system of equations, the classification and solution depend on the relationships between the equations: - **Inconsistent**: The equations have no solutions. - **Consistent dependent**: The equations are dependent on one another and have infinitely many solutions. - **Consistent independent**: The equations are independent and have a unique solution.
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