The relationship between the legislative and executive branches is an important element in the design of a political system. Witness France, where voters elected a new President, the independent Emmanuel Macron, in two rounds of voting in April-May 2017.
France is a unitary republic with a bicameral legislature and a fairly unique, elaborately interconnected “semi-presidential” dual executive designated in two distinct manners: a president is elected directly after one or two rounds of voting (the winning candidate must receive an absolute majority of votes, which almost guarantees that the two candidates receiving the highest total of votes in a first round of voting will square off in a second round); and a prime minister is appointed by the President on the basis of the outcome of elections to the lower house of the legislature (where victorious candidates are elected in a variation of first past the post).
The President can dissolve Parliament and call early elections, while the Parliament can dismiss the Prime Minister, who forms a classic parliamentary government. Should the President and Prime Minister hail from two different parties, the result is what the French call cohabitation.
Legislative elections will now be held in two rounds in June 2017.
This note from the US Library of Congress explains the French system well. Additional background here and here.
The Joy of Politics 