Suppose I have a multivariate linear equation (of an arbitrary number of variables, for this example, say 4): $f(x,y,z,w) = ax+by+cz+dw=n$, where $a,b,c,d$ are constants that I know. And $n$ is the value that I want the LHS to equal (the target). Is there an analytical solution that gives me these values $x,y,z,w$. Or at least a parametric equation if it has multiple solutions?
EDIT: $x,y,z,w \in \mathbb{N \cup {{0}}}$ AND $a,b,c,d \in \mathbb{N \cup {{0}}}$