To solve for $x$, $y$, and $z$, we compare corresponding elements in the two matrices:

$\begin{bmatrix} x+3 & y+4 \\ 7 & 9 \end{bmatrix} = \begin{bmatrix} 5 & -4 \\ 7 & z \end{bmatrix}$

Step 1: Solve for $x$

From the first element: $x + 3 = 5$ $x = 5 - 3 = 2$

Step 2: Solve for $y$

From the second element: $y + 4 = -4$ $y = -4 - 4 = -8$

Step 3: Solve for $z$

From the fourth element: $9 = z$

Final Answer:

$x = 2, \quad y = -8, \quad z = 9$

The correct answer is option D.

Would you like further explanation or a different approach?

Related Questions:

1. How do you determine when two matrices are equal?
2. Can you solve for variables in a 3×3 matrix equation?
3. What happens if matrices have different dimensions—can they be equal?
4. How can you verify solutions in matrix equations?
5. What are some real-world applications of solving matrix equations?

Tip: When solving for variables in matrices, always match corresponding elements carefully!