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Linear Equations with infinite solutions

I have 4 equations with 6 variables, which means I will have 2 free variables, which means I would have infinitely many solutions. I found one solution but I don't know what functions I should use in Sage to generate 10 different solutions (as that is what I was asked to do).

This is what I did: M=matrix(QQ, [[1,2,3,4,5,6],[1,1,1,1,1,1],[1,-1,1,-1,1,-1],[1,2,1,3,1,4]]); x=vector(QQ, [6,1,-1,4]); M.solve_right(x)

It only gives me one solution: 0, -1, 0, 2, 0, 0, how do I get more?