where it would be important to have a set of solutions for the variables, rather than specific answers?

Answer 1

A specific answer works in a specific instance. For example, I can drop something and say it was falling at 9.8 m/s after one second. if I say the velocity of a falling body is 9.8 m/s^2 * s, I can calculate it's velocity at any point during its fall. But that equation only works on earth. If I say it is G * M1 * M2/d^2 * s, it works on all planets.

Answer 2

My hunch is only in mathematics. For example, in electrical engineering we often use complex numbers which, as you probably know, have a real part and an imaginary part. Both parts are necessary for the calculation but, in the end, only the real part describes physical reality. The imaginary part is discarded.

I can't think of a physical situation which can be correctly described by two different solutions, although I can imagine a pair of functions (simultaneous nonlinear equations) whose curves cross in several places.

The above may illustrate the limitations of a specialized education, as I'm an Engineer and not a Mathematician. I don't think I've been much help to you.....

Answer 3

set of solution r the possible solutions for the equation.