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We are given two matrices \( A \) and \( B \) and asked to find the value of \( x + y \) if the matrices are equal, i.e., \( A = B \).

The matrices are as follows:

\[
A = \begin{pmatrix} 2 & x - y \\ 4 & 6 + 2x \end{pmatrix}, \quad B = \begin{pmatrix} 2 & -1 \\ -2x & 2y + 4 \end{pmatrix}
\]

Since the matrices are equal, corresponding elements in both matrices must be the same. Therefore, we can set up the following system of equations by equating the corresponding elements of matrices \( A \) and \( B \):

1. From the first row, first column: 
   \[
   2 = 2 \quad (\text{which is true and gives no new information}).
   \]

2. From the first row, second column:
   \[
   x - y = -1 \quad \text{(Equation 1)}
   \]

3. From the second row, first column:
   \[
   4 = -2x \quad \Rightarrow x = -2 \quad \text{(Equation 2)}
   \]

4. From the second row, second column:
   \[
   6 + 2x = 2y + 4 \quad \text{(Equation 3)}
   \]

Now, substitute \( x = -2 \) from Equation 2 into Equations 1 and 3:

- Substituting into Equation 1:
  \[
  -2 - y = -1 \quad \Rightarrow y = -1
  \]

- Substituting into Equation 3:
  \[
  6 + 2(-2) = 2(-1) + 4 \quad \Rightarrow 6 - 4 = -2 + 4 \quad \Rightarrow 2 = 2
  \]
  This is true, confirming that our values for \( x \) and \( y \) are correct.

Thus, \( x = -2 \) and \( y = -1 \). Therefore:
\[
x + y = -2 + (-1) = -3
\]

The correct answer is **E: -3**.

---

Would you like any further explanation or clarification?

Here are some related questions to explore:
1. What is the condition for two matrices to be equal?
2. How do you solve systems of equations involving matrices?
3. What happens if matrix sizes don't match in equality conditions?
4. How would the solution change if the matrices had more variables?
5. Can you solve for both \( x \) and \( y \) using just one equation?

**Tip**: Always double-check the positions of corresponding elements in matrix equality problems to ensure all constraints are considered.

Diketahui A = [[2, x - y], [4, 6 + 2x]] dan B = [[2, -1], [-2x, 2y + 4]]. Jika matriks A = B, maka nilai x + y adalah?

This matrix equality problem involves solving for the variables x and y when two 2x2 matrices are equal. Detailed step-by-step solutions show how to set up linear equations and solve them to find x + y.

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