Final answer:
You would be living under a Hereditary Monarchy, where a single ruler who inherited power resolves disputes, such as the given scenario of a neighbor's sheep grazing on your land.
Step-by-step explanation:
If you lived in Sparta around 900 BC and had to complain to the city-state's one leader about a problem, such as your neighbor's sheep grazing on your land, you would be living under a form of government that is best described as Hereditary Monarchy.
This type of government is characterized by a single ruler who has inherited power, often through familial line, and has the authority to make decisions and settle disputes such as the one mentioned. The Spartan government evolved over time and while it is famous for its unique system of governance created under the reputed lawgiver Lycurgus, the kind of direct appeal to a single leader as described in your situation suggests a monarchical system where the leader wields centralized power.