I habe added new information. Thanks for your help.

I have added a second reply for better understanding. I appreciate your help.

I have added steeply with additional Information,

Yes, I saw it. But the answers was I should use a framework. I would than change than change set value. But like I wrote it I thought my idea does not satisfy all my needs. Thanks for your help

Thanks. I had short walk. I think I may came up with a solution. If I am right I could set one of these unknown and then solve numerically for the others. Then change the make step with same one solve again. Thanks for the links. It‘s quiet funny that the first one is my own question on stackoverflow. It is one of the few topics which are covered very poorly. Thanks. The solution I thought I had found is not completely satisfying. I am sure I will find. My be I can make my life easier with specific definitions. Thanks for that idea.

I am looking for a 1D Intersect. It is for much easier to convert the user input to parametric form. I totally know how to get to the system of equations. Like I said before the real challenge is to solve the system of equations. That is also why I called the question ,, Solve a set of equations“ and not „ Surface intersection“.

I posted a aswer with more information. I hope is clear now.

Thanks.But the real challenge is to get the app to do it on its own. I am try to right a func with two faces as a parameter wich returns me this intersection. Assemblyman those equations out of the two surfaces is very easy. But how do I get my app solve them.

This equations represent an inspection of two cylinders. The first equations was an intersection of a plane and a cylinder. So I want to intersect two parametric surfaces. Todo this the app has solve this set of equations.

I made a comment to the answer below. I hope it is more clear now.

I very sorry. I wanted to give you an simple example but it was easy. New example: cos(u) = t ; sin(u) = 3 sin(s) ; v = 3 cos(s) u,v,s,t are the unknown. I want to know them all at a state. So I make three functions with one of them as the parameter. I hope it is more clear now.