Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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.
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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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