Let's verify your solution step by step:

The equation is given as:
[ [3x -y] = [12\ 3]. ]

This implies the equations:

1. $3x = 12$
2. $-y = 3$

Step 1: Solve for $x$

From $3x = 12$:
$x = \frac{12}{3} = 4.$
This matches your calculation.

Step 2: Solve for $y$

From $-y = 3$:
$y = \frac{3}{-1} = -3.$
This also matches your calculation.

Final Verification

The solutions are:
$x = 4 \quad \text{and} \quad y = -3.$

Yes, your values for $x$ and $y$ are correct. Well done! 😊

Would you like further clarification or to explore related problems? Here are some questions to expand on this topic:

1. What does the matrix equality imply geometrically in this case?
2. How do you handle systems of equations with more than two variables?
3. What if the system were $[3x -y] = [12\ z]$? How would you find $z$?
4. How can you represent this system using augmented matrices and solve it?
5. What happens if the matrix equality includes inequalities instead?

Tip: Always double-check your arithmetic, especially when solving for negative variables.