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.