I'd like to solve a problem just like you. Let me pretend I have been given the equation:
a + b + c + d = 5
Can I determine all 4 variables? Is there any way I can learn the value of all 4 variables, given ONLY that one equation? So one data point only? The answer of course is no. At best you can pick the value of any three of those variables. Set them equal to any number you want. Then you can solve for the one variable you have not specified. That is the fundamental nature of an underdetermined problem - the one equation does not provide sufficient information.
If you have MULTIPLE data points, this becomes a different question. So if you have sufficient data points, then you can solve the problem. But you have said you have only one data point. (And I'm sorry, but the nice flowchart you have shown in a comment is not going to make the mathematics work.) An underdetermined problem is just that.
