Closed morphism of products of k-schemes with a field extension of k implies closed

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This is from exercise 9.2.J of Ravi Vakil's notes on algebraic geometry here

We have a morphism of $k$ schemes $\pi:X \rightarrow Y$. $l/k$ is a field extension. We want to show if $\pi\times_k l: X\times_k l\rightarrow Y\times_k l$ is a closed embedding then $\pi$ also is one.

If you assume $\pi$ is affine this is fairly simple. I am having a lot of trouble proving it without that hypothesis. Any help would be appreciated.