Transforming a linear constraint.

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I have two variables $x$, and $y$. That are related by $Bx=y$. There is also a linear inequality constraint on $x$: $Ax \leq b$. Is it possible to write down the feasible set of $y$ as a linear inequality constraint? How would I do this? I also know that the columns of $A$ are linearly independent, but I don't have any such condition on $B$.