https://file.aiquickdraw.com/mathbot/file/1726649899599p6646frk.jpg

The image contains the following system of linear equations:

\[
\begin{aligned}
x_1 + x_2 + 2x_3 &= 9 \\
2x_1 + 4x_2 - 3x_3 &= 1 \\
3x_1 + 6x_2 - 5x_3 &= 0
\end{aligned}
\]

I will now solve this system using an appropriate method (e.g., Gaussian elimination). Let's start by expressing this as an augmented matrix and proceed with the solution.The solution to the system of equations is:

\[
x_1 = 1, \quad x_2 = 2, \quad x_3 = 3
\]

This was solved using Gaussian elimination.

Would you like further details on the steps, or have any other questions? Here are some related questions you might explore:

1. How does Gaussian elimination work step by step?
2. Can you show an alternative method, like Cramer's rule?
3. What is the determinant of this system’s coefficient matrix?
4. How does the rank of a matrix affect the solvability of a system of equations?
5. What if the system had no solution or infinitely many solutions?

**Tip:** When solving systems of equations, checking the determinant of the coefficient matrix can help determine if the system has a unique solution.

Solve the system of linear equations using Gaussian elimination.

Learn how to solve a system of linear equations involving three variables using Gaussian elimination. This detailed guide provides steps to form the augmented matrix, perform row reductions, and discuss the solution's uniqueness. Suitable for introductory courses in linear algebra at the university level.

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