https://file.aiquickdraw.com/mathbot/file/1725623818182234krkwn.jpg

The system of equations provided in the image is:

\[
\begin{cases}
-2x - 6y - 9z = 5 \\
-2x - 5y - 8z = 5 \\
5x + 15y + 25z = 1
\end{cases}
\]

We need to solve this system for \(x\), \(y\), and \(z\).

Let me compute the solution by solving this system of equations.The solution to the system of equations is:

\[
x = -\frac{53}{5}, \quad y = -\frac{27}{5}, \quad z = \frac{27}{5}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you determine if a system of equations has a unique solution?
2. What methods can be used to solve systems of linear equations?
3. How can you verify if a solution satisfies all equations in a system?
4. Can a system of linear equations have no solution or infinitely many solutions?
5. How does substitution differ from elimination in solving linear systems?

**Tip:** When solving systems, try using matrix methods like Gaussian elimination for larger systems.

The system of equations is:

-2x - 6y - 9z = 5
-2x - 5y - 8z = 5
5x + 15y + 25z = 1

Learn how to solve a system of linear equations with three variables. The example provided includes a system with equations in x, y, and z, and uses methods like Gaussian elimination to find the solution. Suitable for students in Grades 10-12.

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