Final answer:
Athens and Sparta led the Greek city-states in setting aside their differences to combat the Persian invasions during the Persian Wars. The collaboration, strategic military actions, and victories of the Greeks under the Hellenic League eventually led to the withdrawal of Persian forces and the recognition of Ionian independence.
Step-by-step explanation:
The Greek city-states, notably Athens and Sparta, put aside their differences to fight against the invading Persians. The conflict, known collectively as the Persian Wars, began when the Greek cities of Ionia rose up against Persian rule, prompting the Persian king Darius to target both the Ionian cities and their Athenian supporters. Darius's son, Xerxes I, later continued the campaign against Greece, which saw major battles at Marathon, Thermopylae, and finally Plataea where the Greek coalition forces, led by the Spartans, achieved a decisive victory.
The alliance, sometimes known as the Hellenic League, saw the Spartan-led land forces working in conjunction with the Athenian-led naval forces. They successfully defeated the Persian forces through a combination of well-motivated hoplite warriors and strategic defensive stands, despite the Persians fielding considerably larger armies.
The solidarity of the Greek city-states and their victories ultimately led the Persian Empire to abandon its attempts to conquer Greece, recognizing the independence of the Ionian city-states and thus concluding the Persian Wars in favor of the Greeks.