You are solving the equations independently of each other. You solve eqn1 for x1, which leaves it expressed in terms of x2 and x3. You solve eqn2 for x2, which leaves it expressed in terms of x1 and x3 -- and so on.
To proceed iteratively, once you have solved eqn1 for x1, you should substitute that value of x1 into eqn2, transforming it into an equation in x2 and x3; solve for x2 which will be in terms of x3. Then substitute the x1 you found into eqn3 and then substitute the x2 into the result, to get eqn3 in terms of just x3; solve. Now do back substitution.