Question: How to extract the correct vector solution from a set of possible vector solutions?

While I was solving a set of equation using solve function in maple 17, I got a long list of solution set. I want that solution whose components sum to 1. How to extract that solution.

e.g. solve({b[1] = 0, b[2] = 0, b[3] = 0, b[4] = 0, b[5] = 0, b[6] = 0}, {gamma[1], gamma[2], gamma[3], gamma[4], gamma[5], gamma[6]}); where b[i]=0 is a linear equation interms of gamma[1], gamma[2], gamma[3], gamma[4], gamma[5] and gamma[6].

When I use fsolve in place of solve the program was running endlessly.

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