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Let's work through the given problem step by step.

You are given matrices \( A \), \( B \), and \( C \), and asked to find \( x + y \) based on the equation:

\[
A + B = C
\]

The matrices are:

\[
A = \begin{bmatrix} x - 3 & 2 \\ 3 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} x & 3 \\ 2 & y + 2 \end{bmatrix}, \quad C = \begin{bmatrix} 3 & 5 \\ 5 & 4 \end{bmatrix}
\]

Now, summing matrices \( A \) and \( B \):

\[
A + B = \begin{bmatrix} (x - 3) + x & 2 + 3 \\ 3 + 2 & 5 + (y + 2) \end{bmatrix} = \begin{bmatrix} 2x - 3 & 5 \\ 5 & y + 7 \end{bmatrix}
\]

We are told that \( A + B = C \), so:

\[
\begin{bmatrix} 2x - 3 & 5 \\ 5 & y + 7 \end{bmatrix} = \begin{bmatrix} 3 & 5 \\ 5 & 4 \end{bmatrix}
\]

From this, we can compare corresponding elements of the matrices:

1. \( 2x - 3 = 3 \)
2. \( y + 7 = 4 \)

### Solving for \( x \):
\[
2x - 3 = 3
\]
\[
2x = 6
\]
\[
x = 3
\]

### Solving for \( y \):
\[
y + 7 = 4
\]
\[
y = 4 - 7 = -3
\]

Now, the question asks for \( x + y \):

\[
x + y = 3 + (-3) = 0
\]

Thus, the value of \( x + y \) is \( \boxed{0} \).

Please let me know if you'd like any further details or clarifications.

---

Here are five related questions to expand your understanding:
1. What happens if you change the matrix \( A \) to a different size?
2. How would this problem change if \( A + B = 2C \)?
3. Can you generalize the process of matrix addition for \( n \times n \) matrices?
4. What properties of matrix addition are used in this problem?
5. How would you approach this if you were dealing with 3x3 matrices instead of 2x2?

**Tip:** Always ensure that matrices are of the same dimensions before performing matrix operations like addition or subtraction.

Diketahui matriks A = [[x - 3, 2], [3, 5]], B = [[x, 3], [2, y + 2]], dan C = [[3, 5], [5, 4]]. Jika A + B = C, maka tentukan x + y.

Learn how to solve for x and y in the matrix equation A + B = C where matrices A, B, and C are provided. This problem explores matrix addition and basic algebraic equations. Suitable for students in Grades 10-12.

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