By using the supersymmetric version of the Faddeev-Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In this approach the HubbardX-operators are used as field variables. In this framework, we first study the spinless fermion model which satisfies the graded algebra spl(1,1).Later on, in order to satisfy the HubbardX-operators commutation rules satisfiying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for the t-J model are found.This model is also analyzed in the context of the path-integral formalism, and so the correlation generating functional and the effective Lagrangian are constructed.

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