A system of government where an executive branch is led by a president who serves as both head of state and head of government. In such a system, this branch exists separately from the legislature, to which it is not responsible and which it cannot, in normal circumstances, dismiss. system of government where an executive branch is led by a president who serves as both head of state and head of government. In such a system, this branch exists separately from the legislature, to which it is not responsible and which it cannot, in normal circumstances, dismiss.