The first compromise that was brought up at the Constitutional Convention was the Great Compromise. The Great Compromise made it so each state's population would factor in how many representatives in the House they would be getting. It also made it so each state would get two representatives in the Senate.
The second compromise that was brought up at the Constitutional Convention was the Three-Fifths Compromise. This issue of slaves going into the total population of a state was brought up after the Great Compromise gave more representatives to states that had a greater population. Southern states wanted to count slaves in their total population in order to obtain more representatives, but some people disagreed. The Three-Fifths Compromise made it so each slave counted as three-fifths of a free individual.
Both of these affected the government by making the number of representatives based on the population of a state and addressed the problem of slaves counting towards the population.