Question: Eliminating redundant equations

I have a system of 16 polynomial equations in 15 variables. Independently I know there is at least a one parameter familiy of solutions to this system, so there is reason to think at least two of the equations are redundent. I would like to use Maple to decipher which of the equations are redundent, but I am unsure how to proceed.

So far I have looked at the Groebner package, and it seems like the Reduce and InterReduce commands will be useful. Say I call the set of 16 polynomials X and define a lexicographical order T on the variables. I then ask maple to compute

Reduce(X,X,T)

and receive a list with 7 zeroes and 9 polynomials. What exactly is this telling me? Does this mean that maple has used polynomial division and found that 7 of the equations are redundent?

Thanks for your help!