Show that an affine subspace of $\mathbb{R}^d$ is a Borel set.

Question

Everything is in the title.

I was thinking of using the fact that an affine subspace of $\mathbb{R}^d$ is the set of solutions to a system of linear equations, but I can't figure out how to describe those solutions in a way that helps.

I am quite new to affine subspaces so I don't really know where to start.

Thanks :)