Question: can a country have both a president and a prime minister

Answer: Yes, A semi-presidential system or dual executive system is a system of government in which a president exists alongside a prime minister and a cabinet, with the latter being responsible for the legislature of a state. It differs from a parliamentary republic in that it has a popularly elected head of state, who is more than a purely ceremonial figurehead, and from the presidential system in that the cabinet, although named by the president, is responsible to the legislature, which may force the cabinet to resign through a motion of no confidence.