The question is asking for the values of $x$ and $y$ that satisfy the given matrix equation:

$\begin{pmatrix} 2 & 4 \\ 3 & 5 \end{pmatrix} + \begin{pmatrix} 1 & -3 \\ -3x & 4y + x \end{pmatrix} = \begin{pmatrix} 3 & 1 \\ -9 & 17 \end{pmatrix}$

Let's break it down by equating each element of the matrices on both sides.

Step 1: Set Up Equations by Element-Wise Comparison

1. For the element in the first row, first column: $2 + 1 = 3$ This equation is satisfied without needing $x$ or $y$.

2. For the element in the first row, second column: $4 + (-3) = 1$ This equation is also satisfied without needing $x$ or $y$.

3. For the element in the second row, first column: $3 + (-3x) = -9$ Simplifying, we get: $-3x = -12 \Rightarrow x = 4$

4. For the element in the second row, second column: $5 + (4y + x) = 17$ Substitute $x = 4$: $5 + (4y + 4) = 17$ $4y + 9 = 17$ $4y = 8 \Rightarrow y = 2$

Solution

The values of $x$ and $y$ are $x = 4$ and $y = 2$.

Answer

The correct option is C. 4 dan 2.

Would you like a further breakdown of any step?

Here are some related questions:

1. How do you solve for variables in a system of linear equations using matrices?
2. What are the rules for adding matrices element-wise?
3. How do you verify solutions in matrix equations?
4. Can matrices with different dimensions be added or subtracted?
5. What other methods exist to solve for unknowns in matrix equations?

Tip: Always verify each element in a matrix equation individually to ensure all parts are satisfied.