Summary: Using the qualitative theory of ordinary differential equations, we give a qualitative analysis to a two-dimensional plane autonomous system which is equivalent to the Burgers-Korteweg-de Vries equation. Then applying the theory of commutative algebra and the first-integral method, we obtain exact solutions to the Burgers-Korteweg-de Vries equation. The results indicate that the solutions obtained in the literature are the particular cases of our results.