Who was at the Potsdam Conference and why did the participants change in the middle?
President Harry Truman, Joseph Stalin, and Winston Churchill, who left in the middle because he lost the election in Britain and therefore lost power.
When Lincoln issued the Emancipation Proclamation, which slaves were freed in law, and did any slaves actually gain immediate freedom? Why?
Only slaves in states in rebellion (the Confederacy) were freed by the Emancipation Proclamation, meaning those in border states that were both slave states and still in the Union remained in slavery. This is for two reasons. First, Lincoln justified the Emancipation Proclamation as a strategic act to weaken the Confederacy and force them back into the Union, and this logic could not apply to the border states. He also did not want to anger the border states to the point that they too left the Union. Few slaves actually gained immediate freedom with the Emancipation Proclamation because they lived in rebellious states who refused to follow the President's order. Most slaves were therefore not freed until the Union army arrived.
Explain why when you have a it takes more than one equation to solve a set of equations with two variables.
Because there are two variables, there could be multiple solutions to the first equation as if you changed the value of one, the value of the other could change to keep the equation true. For example, 5y+3x=11 is true both when y=1 and x=2 and when y=2 and x=1/3.