# Getting all solutions to system linear equation from one solution

I am trying find all solution to dependent system linear equation. Suppose that I have one solution to system linear equation. It's possible modify system linear equation to find other solutions?

EDIT: Thanks for replies.

I specify my equations, Ax = b. Matrix A is square integer matrix size 144. b is vector contains all-6 number. I am looking only 0-1 solution, i.e x=0 or x=1. Number of variables is 144. I found one solution from gurobi optimalization(find only one optimal solution), but I know that exists another solutions. I want to modify system of linear equation. Is it possible?

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What do you know about the general form of a solution to $Ax=b$? –  Dominique Mar 30 '13 at 13:58
You can find the kernel of your system i.e. the solutions to $Ax = 0$. Then with the solution you found ($x_0$) the general solution is $x_0 + \ker A$ –  André Mar 30 '13 at 14:03