https://file.aiquickdraw.com/mathbot/file/1727230455174de2bhp5f.jpg

The image shows a system of linear equations. Here is the set of equations extracted from the image:

\[
\text{Given:}
\]

\[
\begin{aligned}
1. &\ \ 3x_1 + x_2 + 7x_3 + 9x_4 = 4 \\
2. &\ \ -x_1 + x_2 + 4x_3 + x_4 = 7 \\
3. &\ \ -2x_1 - 2x_3 - 3x_4 = 0 \\
4. &\ \ -x_2 - 4x_3 - 6x_4 = 6 \\
\end{aligned}
\]

This is a system of four equations with four unknowns: \(x_1, x_2, x_3, x_4\). Would you like me to solve this system using a particular method (e.g., Gaussian elimination, substitution, etc.), or do you have a specific approach in mind? 

Also, let me know if you'd like a detailed explanation of each step. 

Here are some questions related to solving systems of linear equations:
1. What is the Gaussian elimination method?
2. How can matrix operations help solve systems of linear equations?
3. What are the possible solutions for a system of linear equations?
4. How can we check if a system is consistent or inconsistent?
5. What is the determinant's role in determining a system's solvability?

**Tip**: When solving a system of equations, always check if it is consistent by looking for contradictions in the equations.

Solve the system of linear equations shown in the image.

Learn how to solve a system of linear equations with four variables: 3x_1 + x_2 + 7x_3 + 9x_4 = 4, -x_1 + x_2 + 4x_3 + x_4 = 7, -2x_1 - 2x_3 - 3x_4 = 0, and -x_2 - 4x_3 - 6x_4 = 6. This detailed solution covers Gaussian elimination and matrix representation methods, suitable for students in Grades 10-12.

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