https://file.aiquickdraw.com/mathbot/file/17250862755443ovft5cm.jpg

It looks like you've uploaded the same image again. Based on the image you provided earlier, the system of equations is:

\[
\begin{cases}
x_1 + x_2 + 2x_3 = 2 \\
3x_1 + 2x_2 - 3x_3 = 1
\end{cases}
\]

We've already solved this system and found the general solution:

\[
\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix}
=
\begin{bmatrix}
7t - 3 \\
5 - 9t \\
t
\end{bmatrix}
\]

where \( t \) is a parameter.

If you're looking for something specific that wasn't addressed in the previous solution, or if you have a different question related to this problem, feel free to ask!

Would you like more details or have any questions? Here are some related questions you might find helpful:

1. How can you verify the solution to a system of linear equations?
2. What is the geometric interpretation of a system with infinite solutions?
3. How does matrix rank affect the solution to a system of equations?
4. Can the same methods used here be applied to non-linear systems?
5. What are some practical applications of solving systems of linear equations?

**Tip:** Always double-check the coefficients in your matrix when setting up a system of equations to avoid calculation errors later on.

Explore the detailed solution and general solution for a system of linear equations. This problem involves key concepts like matrix operations and solving systems of linear equations with parameters. Suitable for advanced high school or college students.

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