The answer to this in my opinion would be multi-faceted. For example, it could involve an equation that was written such that there is no singular answer. Or it could be a system of equations with too many unknowns. If that is the case then there is no unique answer. You can get an answer, but because there are multiple answers that work, it is not solvable.
when you solve differential equations, you get answers that can be the general solution where you are not solving for the initial conditions or boundary conditions or in other words the constant. In these cases solutions or linear combinations of the solutions are also solutions. For example, if you multiply a solution by some constant and add or subtract some constant, it is still a solution. These cases are solvable and even though you are solving for the general case and there are multiple answers, they are indeed solvable.
if you have a system of equations and in one equation it requires some variable to be one value but a different value in another equation within the system then it is unsolvable.
if your equation divides by a zero when solving, it is unsolvable.
This is not intended to be an all-inclusive list.
Example:
Solve for m when x = 0:
y = m*x
In this case, m is undefined at x = 0. Note that it is not possible to solve for m in terms of y when x = 0 because y/0 is undefined.
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