Final answer:
The Daugava River flows through Riga, Latvia, and empties into the Gulf of Riga in the Baltic Sea, not into the Gauja River. The Gauja is actually a tributary of the Daugava.
Step-by-step explanation:
The river that flows through Riga, Latvia, is called the Daugava River, also known as the Western Dvina. It is important to clarify that the Daugava River does not empty into the Gauja River; rather, the Gauja River is a tributary of the Daugava. The Daugava flows through Latvia and is a major river in the Baltic region that eventually empties into the Gulf of Riga of the Baltic Sea, not the Gauja River.
In terms of importance, rivers like the Daugava are vital for trade and transportation in Europe, connecting many cities and regions. The Gauja River also plays a significant role as a tributary for the Daugava, contributing to its flow as it makes its way to the sea. The significance of rivers in Europe can be seen with examples like the Volga, which provides transportation and fresh water in Russia, and the Rhine and Danube, which are major waterways for commerce and travel.