https://file.aiquickdraw.com/mathbot/file/1726500365059x80v37br.jpg

Let's analyze and solve the system of equations from the image.

The system is:

\[
\begin{cases}
x_1 + 4x_3 + 3x_4 = 26 \\
x_2 - 3x_3 - 3x_4 = -26 \\
2x_1 - 2x_2 + 10x_3 + 12x_4 = 76 \\
-x_2 + 3x_3 + 9x_4 = 26
\end{cases}
\]

We will solve this system step by step.

### 1. Equation 1:
\[
x_1 + 4x_3 + 3x_4 = 26
\]

### 2. Equation 2:
\[
x_2 - 3x_3 - 3x_4 = -26
\]

### 3. Equation 3:
\[
2x_1 - 2x_2 + 10x_3 + 12x_4 = 76
\]

### 4. Equation 4:
\[
-x_2 + 3x_3 + 9x_4 = 26
\]

Now, let's solve this system for \(x_1, x_2, x_3, x_4\). I will begin by applying methods like substitution or elimination. Let me calculate this.The correct solution to the system of equations is:

\[
x_1 = -2, \quad x_2 = -5, \quad x_3 = 7, \quad x_4 = 0
\]

It seems the provided answers \(x_2 = 13\), \(x_3 = 1\), and \(x_4 = 8\) are incorrect.

Would you like further details or clarifications? Here are some related questions for you:

1. How can you verify the solution of a system of equations?
2. What is the method of substitution, and how does it apply to solving systems?
3. How does the elimination method work for solving systems of linear equations?
4. What are the advantages of using matrix methods (e.g., Gaussian elimination) for larger systems?
5. Can systems of equations have no solution, and how do you identify such cases?

**Tip:** Always substitute your solution back into the original system to verify correctness.

Solve the system of equations: 
1. x1 + 4x3 + 3x4 = 26 
2. x2 - 3x3 - 3x4 = -26 
3. 2x1 - 2x2 + 10x3 + 12x4 = 76 
4. -x2 + 3x3 + 9x4 = 26

Solve a system of four linear equations step by step. This problem focuses on key linear algebra concepts, such as substitution and elimination methods, making it suitable for students in Grades 10-12.

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