In this research paper, we prove the following theorem for the general case of trapezoidal fuzzy numbers: A fully fuzzy linear programming problem of equality constraints containing all the parameters are trapezoidal fuzzy numbers has fuzzy basic feasible solution if it has fuzzy feasible solution. Next, we develop a fuzzy algebraic method for obtaining the solutions of fully fuzzy linear programming problems, which contains trapezoidal fuzzy numbers, without converting them into crisp linear programming problems. Particularly in this method, we use the modified operations of subtraction and division of trapezoidal fuzzy numbers. Finally, we illustrate the algorithm by solving some problems.