Of the options that you have given us, the best choice is "parliamentary system." It is possible that this would be true of a constitutional republic, but it is not necessarily so.
In a parliamentary system (perhaps the one best known to Americans is that of the United Kingdom), there is no separate executive branch. The executive is, instead, drawn from members of the legislative branch. In England today, David Cameron is actually a Member of Parliament in addition to being the Prime Minister. There is no separate election in which the people of the country voted for or against him.