Compute the following limit if it exist $\lim_{(x, y) \to (0,0)} \frac{sin(xy)}{y}$

Question

$\lim_{(x, y) \to (0,0)} \frac{sin(xy)}{y}$

Solution:

$\lim_{(x, y) \to (0,0)} \frac{sin(xy)}{y} = \lim_{(x, y) \to (0,0)} \frac{sin(xy)}{xy} \lim_{(x, y) \to (0,0)} x = 1 \lim_{(x, y) \to (0,0)} x = 0$

could someone explain this solution please