Final answer:
The Seventeenth Amendment illustrates the American system's blend of republican and democratic elements through its establishment of the direct election of U.S. Senators by the people, replacing the previous method of selection by state legislatures.
Step-by-step explanation:
The Seventeenth Amendment of the United States Constitution is a key example that illustrates how America functions as both a republic and a democracy. This amendment, passed in 1913, shifted the election of U.S. Senators from being selected by state legislatures to a process of direct election by the people of the states they represent. This transition from an indirect to a direct form of representation exemplifies the combination of a republic, where sovereignty is held by the people and their elected representatives, and a democratic value of allowing citizens to directly influence their leadership and governance.