Find Set of Solutions For Rank-Deficient Linear System

Question

I have a matrix $A\in\mathbb{R}^{n\times n}$ that is rank-$(n-1)$. I would like to find the general solution to the linear system $Ax=b$, where $b\in \mathbb{R}^n$. $A$ is rank-deficient, so there is not a unique solution. I believe that, since the rank of $A$ is $(n-1)$, any solutions to my linear system must lie on some line. If this is true, I would like to find this line. If not, I would like to find some other way to characterize the set of solutions to my rank-deficient linear system. I was hoping someone might help by pointing me in the right direction on this problem. Thank you.