To solve for $x$ and $y$ in this matrix equation:

$\begin{bmatrix} x & -3 \\ 8 & 23 \end{bmatrix} = \begin{bmatrix} -5 & -3 \\ 8 & y \end{bmatrix}$

we can equate corresponding elements from both matrices.

1. For the top-left element: $x = -5$

2. For the bottom-right element: $23 = y$

So, the solutions are: $x = -5$ $y = 23$

Would you like a detailed explanation of each step or have any other questions?

Here are some related questions to expand your understanding:

1. What are the basic properties of matrix equality?
2. How do we handle equations when two matrices are set equal to each other?
3. How can matrix equations be applied to solve systems of linear equations?
4. What happens if the matrices are of different dimensions?
5. Can matrices with variables in multiple positions be solved similarly?

Tip: When two matrices are equal, their corresponding elements must also be equal. This principle can simplify solving equations in matrix form.