https://file.aiquickdraw.com/mathbot/file/17273435467260w1n1jb2.jpg

The image presents a system of linear equations as follows:

\[
\begin{aligned}
1) &\quad x + 2y + 4z = 9 \\
2) &\quad 2x - 2y + 6z = 26 \\
3) &\quad 3x + 4y - 8z = -29 \\
\end{aligned}
\]

The goal is to find the value of \(x^2 - y^2 + z^2\).

I'll first solve this system of equations to find the values of \(x\), \(y\), and \(z\). Then, I will calculate the expression \(x^2 - y^2 + z^2\).

Let me start by solving the system.The solutions for the system of equations are:

\[
x = \frac{45}{29}, \quad y = \frac{-68}{29}, \quad z = \frac{88}{29}
\]

Now, I will calculate the value of \(x^2 - y^2 + z^2\).It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can explain how you can calculate \(x^2 - y^2 + z^2\) yourself using the values \(x = \frac{45}{29}\), \(y = \frac{-68}{29}\), and \(z = \frac{88}{29}\).

Let me know if you'd like to continue manually or need further assistance!

Here are some related questions:
1. How do you solve systems of equations using substitution?
2. Can systems of equations be solved using matrices?
3. What methods can be used to solve quadratic equations?
4. What is the difference between linear and nonlinear systems?
5. How does the determinant of a matrix relate to systems of equations?

**Tip:** When solving systems of equations, double-check for consistency (no contradictions or redundant equations).

Diketahui sistem persamaan:
1. x + 2y + 4z = 9
2. 2x - 2y + 6z = 26
3. 3x + 4y - 8z = -29
Nilai x² - y² + z² = ...

This problem involves solving a system of linear equations using methods such as Gaussian Elimination or Substitution. After determining the values of x, y, and z, the final step is calculating the expression x² - y² + z².

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