https://file.aiquickdraw.com/mathbot/file/1727077334751luqsgf2i.jpg

The problem in the image asks to find the values of \(x\) and \(y\) in the following matrix equation:

\[
\begin{pmatrix} 2 & 1 \\ 1 & -3 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 13 \\ -4 \end{pmatrix}
\]

This is a system of linear equations, which can be expanded as follows:

1. For the first row: 
   \[
   2x + 1y = 13
   \]

2. For the second row:
   \[
   1x - 3y = -4
   \]

### Solving the system of equations:

1. From the second equation:
   \[
   x - 3y = -4 \quad \Rightarrow \quad x = 3y - 4
   \]

2. Substitute \(x = 3y - 4\) into the first equation:
   \[
   2(3y - 4) + y = 13
   \]
   Simplify:
   \[
   6y - 8 + y = 13
   \]
   \[
   7y - 8 = 13
   \]
   \[
   7y = 21 \quad \Rightarrow \quad y = 3
   \]

3. Substitute \(y = 3\) into \(x = 3y - 4\):
   \[
   x = 3(3) - 4 = 9 - 4 = 5
   \]

Thus, \(x = 5\) and \(y = 3\).

The correct answer is **B. 5 dan 3**.

Would you like more details on solving this type of matrix equation or have any questions?

### Related Questions:
1. How can we solve a system of linear equations using matrices?
2. What are the properties of matrix multiplication?
3. How do we verify the solution to a system of equations in matrix form?
4. What is the determinant of a 2x2 matrix, and why is it important?
5. How can Cramer's rule be applied to solve 2x2 systems of equations?

### Tip:
When solving a system of linear equations in matrix form, you can also use inverse matrices if they exist, which provides another method to find the solution.

Nilai x dan y pada persamaan matriks (2 1; 1 -3) * (x y) = (13 -4)

Solve the system of linear equations using a 2x2 matrix. The problem involves solving the matrix equation (2 1; 1 -3) * (x y) = (13 -4) step by step, including substitution and matrix multiplication. Suitable for high school students in Grades 10-12.

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