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The system of equations was solved using the Gauss-Jordan method, resulting in the reduced matrix:

\[
\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{pmatrix}
\]

This means the system has no unique solution, as the result indicates a contradiction or degeneracy in the system. Specifically, this corresponds to a situation where the system is either inconsistent or dependent.

Do you want details or have any questions?

Here are 5 related questions to explore further:
1. What happens if the system of equations is inconsistent?
2. How can you recognize a system that has infinitely many solutions?
3. What is the difference between Gaussian elimination and Gauss-Jordan elimination?
4. How do we interpret a homogeneous system in terms of matrix solutions?
5. Can you apply Gauss-Jordan to systems with more variables?

**Tip:** When using the Gauss-Jordan method, the system is reduced to its simplest form, making it easy to check for unique, infinite, or no solutions.

Solve the system of linear equations using the Gauss-Jordan method: 9x + 10y = 11, 13x + 14y = 15, 21x + 22y = 23

This article explains how to solve the system of equations 9x + 10y = 11, 13x + 14y = 15, 21x + 22y = 23 using the Gauss-Jordan elimination method. Follow a step-by-step solution to reduce the system to row echelon form and find whether the system has a unique solution, infinite solutions, or no solution.

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