Manage the value of $m,n$ in between $0$ and $1$ in the following equations.

Question

Let us consider the equations $$ax+by=m$$ $$cx+dy=n.$$ I have values for $(a,b,c,d)$ and $(x,y)$.
Then clearly I got the values $(m,n)$. But what I need to do, I want the values $(m,n)$ in between $(0,1)$, that is, both of $m,n$ must lie in the interval $(0,1)$. But I can only change the values of $x$ and $y$, and the values for $(a,b,c,d)$ is given constant, cannot be changed. And also $(m,n)$ is unknown for us. So how can I manage $x,y$ so that $m,n \in (0,1)$?
Basically I can use the function $f(x)=\frac{1}{1+e^{-x}}$ which takes value from $0$ to $1$, but I cannot understand where to use this function, since $m,n$ are unknown to us and only we can tune the value of $x,y$.
I can do it by trial but what if there are $100$ equations instead of $2$? Please help me to solve this in general. Thanks.