Degrees of Freedom is the number of values in the final calculation of a statistic that are free to vary.
For the problem
a + 2b + 3c = d
we three degrees of freedom. We can choose the values for three variables and then the fourth variable is locked by our choices. Well, I hope that is the answer.
For a system of equations, you have degrees of freedom if there are more variables than equations. This assumes that all your equations are all linearly independent (of each other).
This is the one page, that I regret starting it.