https://file.aiquickdraw.com/mathbot/file/1729058704608b3oj8ptx.jpg

The system of linear equations shown in the image is as follows:

\[
\begin{align*}
x_2 + x_3 + x_4 &= 0 \tag{1}\\
3x_1 + 3x_3 - 4x_4 &= 7 \tag{2}\\
x_1 + x_2 + x_3 + 2x_4 &= 6 \tag{3}\\
2x_1 + 3x_2 + x_3 + 3x_4 &= 6 \tag{4}
\end{align*}
\]

This is a system of four equations with four unknowns: \(x_1\), \(x_2\), \(x_3\), and \(x_4\). To solve this system, we can use methods like substitution, elimination, or matrix techniques such as Gaussian elimination. Would you like me to proceed with solving it step by step?

Let me know if you'd like details on a specific method.

### Questions:
1. Do you want to solve this system using substitution or Gaussian elimination?
2. Are you interested in the matrix representation of this system?
3. Would you like a step-by-step solution, or just the final values of the variables?
4. Do you prefer solving this system symbolically or numerically?
5. Are you familiar with how to interpret the solution of a system of linear equations?

### Tip:
For large systems of equations, matrix methods (like Gaussian or Gauss-Jordan elimination) are often faster and less error-prone than manual substitution or elimination methods.

Solve the following system of linear equations:
1. x2 + x3 + x4 = 0
2. 3x1 + 3x3 - 4x4 = 7
3. x1 + x2 + x3 + 2x4 = 6
4. 2x1 + 3x2 + x3 + 3x4 = 6

Learn how to solve a system of four linear equations with four unknowns using methods like Gaussian elimination and substitution. This problem involves concepts from linear algebra, making it ideal for students in Grades 10-12.

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