Which of the following acts of congress contributed to an increase in settlement in the west by granting free land to individuals after they had lived on it for five years?

This was called the Homestead Act, and it opened the way for numerous Americans to own land in the newly occupied West. This helped both the settler and the government.

They made a checks and balance system to equal power within the branches. the "check" meant that one branch would watch one branch and "balance" them if they were too powerful. if you want more info on this, i would just google checks and balance system.