https://file.aiquickdraw.com/mathbot/file/17269833327658x3byquo.jpg

The image shows a system of linear equations in three variables (SPLTV) with the goal of determining the value of \( y \). The system is:

\[
\begin{aligned}
1. & \quad x - 3y + 2z = 9 \\
2. & \quad 2x + 4y - 3z = -9 \\
3. & \quad 3x - 2y + 5z = 12 \\
\end{aligned}
\]

We will solve this system of equations using substitution or elimination to find the value of \( y \).

Let me calculate this for you.The value of \( y \) that satisfies the system of equations is \( y = -2 \). Therefore, the correct answer is:

**(C) -2**

Would you like further details on the solution process or have any other questions?

Here are five related questions to explore:

1. How can we solve a system of three equations using substitution?
2. How does the elimination method work for systems of three variables?
3. What are some common methods for solving systems of linear equations?
4. Can this system be solved using matrix operations like Gaussian elimination?
5. What happens if a system of equations has no solution or infinitely many solutions?

**Tip:** When solving systems of equations, always check if the system is consistent or inconsistent (i.e., has one solution, no solution, or infinitely many).

Find the value of y that satisfies the system of linear equations (SPLTV):
1. x - 3y + 2z = 9
2. 2x + 4y - 3z = -9
3. 3x - 2y + 5z = 12

Solve a system of three linear equations: x - 3y + 2z = 9, 2x + 4y - 3z = -9, and 3x - 2y + 5z = 12 to find the value of y. Learn the solution using elimination and substitution methods. Suitable for students in Grades 10-12.

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