Solve the system by row-reducing the corresponding augmented matrix. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) S2x + y = 19 \x + y = 14 (х, у) %3D
Solve the system by row-reducing the corresponding augmented matrix. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.) S2x + y = 19 \x + y = 14 (х, у) %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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11.
![**Solve the System of Equations by Row Reduction**
Solve the system by row-reducing the corresponding augmented matrix. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
\[
\begin{cases}
2x + y = 19 \\
x + y = 14
\end{cases}
\]
\((x, y) = \left( \boxed{} \right)\)
**Explanation**:
- The given system of equations can be solved by converting it into an augmented matrix and using row reduction techniques (Gaussian elimination) to find the solution for \(x\) and \(y\).
- If the system has no solution, it is considered "inconsistent."
- If there are infinitely many solutions, the system is "dependent."
Proceed with solving the system to find the appropriate values for \(x\) and \(y\), or determine if the situation is one of the described cases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d8e838a-6c8b-4033-a5e3-a56465c5aa54%2F07745955-c05e-4018-aa87-841fa0f9ce16%2Fw41tub_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the System of Equations by Row Reduction**
Solve the system by row-reducing the corresponding augmented matrix. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
\[
\begin{cases}
2x + y = 19 \\
x + y = 14
\end{cases}
\]
\((x, y) = \left( \boxed{} \right)\)
**Explanation**:
- The given system of equations can be solved by converting it into an augmented matrix and using row reduction techniques (Gaussian elimination) to find the solution for \(x\) and \(y\).
- If the system has no solution, it is considered "inconsistent."
- If there are infinitely many solutions, the system is "dependent."
Proceed with solving the system to find the appropriate values for \(x\) and \(y\), or determine if the situation is one of the described cases.
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