Step 1 :Given the matrix equation: \(\left(\begin{array}{cc}x & 3 \\ 5 & 2 y\end{array}\right)=\left(\begin{array}{cc}6 & 3 \\ 5 & 8\end{array}\right)\)
Step 2 :Compare the corresponding elements of the two matrices to form equations:
Step 3 :\(x = 6\)
Step 4 :\(2y = 8\)
Step 5 :Solve the equations for x and y:
Step 6 :\(x = 6\)
Step 7 :\(y = \frac{8}{2} = 4\)
Step 8 :\(\boxed{x = 6 \text{ and } y = 4}\)