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Based on the calculations:

- \( x = \frac{1}{2} \)
- \( y = 0 \)
- \( z = -\frac{3}{2} \)

The correct option is:

**Option 3:** \((\frac{1}{2}, 0, -\frac{3}{2})\)

Would you like to delve deeper into any of the steps, or do you have any further questions? Here are some additional questions you may consider:

1. How do you interpret the solution of a system of linear equations geometrically?
2. Can you explain the difference between consistent and inconsistent systems?
3. What are the implications of having free variables in a solution?
4. How does one recognize a unique solution versus infinitely many solutions?
5. Why is row reduction important in solving systems of equations?
6. How can matrix operations be applied to find the inverse of a matrix?
7. What methods exist besides row reduction for solving systems of equations?
8. How does one determine the rank of a matrix?

**Tip:** Always verify your solutions by substituting them back into the original equations to ensure correctness.

Explore how to solve a system of linear equations with a detailed step-by-step solution. This problem covers matrix operations and the application of Gaussian elimination in determining solutions. Suitable for students in Grades 10-12.

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