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We are given two matrices, \( K \) and \( L \), as well as the condition \( K = L \). The matrices are:

\[
K = \begin{pmatrix} 6 & 3 \\ 1 & 5 \end{pmatrix}
\quad \text{and} \quad
L = \begin{pmatrix} 6 & x + 3y \\ 2x - 5 & 5 \end{pmatrix}
\]

We need to find the values of \( x \) and \( y \) such that \( K = L \).

Since \( K = L \), the corresponding elements of these matrices must be equal. Thus, we can set up the following system of equations by comparing the elements:

1. \( 6 = 6 \) (no new information here).
2. \( 3 = x + 3y \)
3. \( 1 = 2x - 5 \)
4. \( 5 = 5 \) (no new information here).

Now, we solve the system of equations:

From equation 3:
\[
1 = 2x - 5
\]
Add 5 to both sides:
\[
6 = 2x
\]
So,
\[
x = 3
\]

Substitute \( x = 3 \) into equation 2:
\[
3 = 3 + 3y
\]
Subtract 3 from both sides:
\[
0 = 3y
\]
Thus, \( y = 0 \).

The values of \( x \) and \( y \) are:
\[
x = 3, \quad y = 0
\]

Would you like any further details or have any questions? Here are 5 related questions you might find useful:

1. How do we verify matrix equality conditions?
2. What happens if one of the variables does not simplify as easily?
3. How do matrices with more than 2x2 elements impact solving for unknowns?
4. How do these concepts apply to larger systems of equations in matrices?
5. Can the determinant of the matrix be used to check consistency?

**Tip:** When comparing matrices for equality, always make sure to match each corresponding element, as they must all be equal.

Diketahui matriks K = \begin{pmatrix} 6 & 3 \\ 1 & 5 \end{pmatrix} dan matriks L = \begin{pmatrix} 6 & x + 3y \\ 2x - 5 & 5 \end{pmatrix}. Jika K = L, maka nilai x dan y berturut-turut adalah ...

Learn how to solve for x and y in a system of linear equations derived from matrix equality conditions. This problem involves comparing corresponding elements of 2x2 matrices and solving the resulting system of equations. Suitable for students in Grades 10-12.

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