## Why is $\mathbb{K}[X] \otimes_{\mathbb{K}} \mathbb{K}[Y] \longrightarrow \mathbb{K}[X \times Y]$ surjective?

I am studying products in the category of affine varieties and I don’t know how to prove that the map

$$\mathbb{K}[X] \otimes_{\mathbb{K}} \mathbb{K}[Y] \longrightarrow \mathbb{K}[X \times Y],$$

where $$X$$ is a affine variety and $$\mathbb{K}[X]$$ is the ring of regular function on $$X$$, is surjective.

I know that if $$W \subset \mathbb{A}^n$$ is a closed subset then $$\mathbb{K}[W] \simeq \mathbb{K}[z_1, \dots,z_n]/I(W)$$ but I can’t link the two results.

Have you any hints?