Given a system of three linear equations in three variables:
$$a_1x + b_1y + c_1z = d_1$$
$$a_2x + b_2y + c_2z = d_2 $$
$$a_3x + b_3y + c_3z = d_3$$
Suppose two equations represent the same line, i.e., one is a multiple of the other:
$$a_2 = k a_1,\quad b_2 = k b_1,\quad c_2 = k c_1,\quad d_2 = k d_1 \quad (k \neq 0)$$
Since two of the three equations are the same, they together act as only one equation.
Hence, the system effectively has only two independent equations in three variables.
$$\boxed{\text{Therefore, the system does not have a unique solution.}}$$
