The given problem provides two matrices, $A$ and $B$, and asks to find the values of $x$ and $y$ such that $A = B$.

Matrix $A$ is: $A = \begin{bmatrix} 2x & -3 \\ 1 & y - x \end{bmatrix}$ Matrix $B$ is: $B = \begin{bmatrix} 10 & -3 \\ 1 & -1 \end{bmatrix}$

Since the two matrices are equal, corresponding elements must be the same.

1. From the top left corner of the matrix: $2x = 10 \quad \Rightarrow \quad x = \frac{10}{2} = 5$

2. From the bottom right corner: $y - x = -1$ Substituting $x = 5$ into the equation: $y - 5 = -1 \quad \Rightarrow \quad y = 4$

Thus, the values are: $x = 5 \quad \text{and} \quad y = 4$

Would you like more detailed steps or explanations?

Here are 5 related questions you might want to explore:

1. How do you find the determinant of a 2x2 matrix?
2. What happens if matrix $A \neq B$? How do you solve for unknowns?
3. Can you solve for multiple variables in larger matrices?
4. How are matrices used in solving systems of linear equations?
5. What are the properties of matrix equality?

Tip: Always remember that two matrices are equal only if all corresponding elements are equal.