Bodies in Equilibrium
When a body is in equilibrium, we can resolve all the forces in any direction, and in each direction we find there are no net forces. If a body has no forces acting on it, it may still move, but it will not accelerate, because by Newton's second law of motion, F=ma, if F=0, a=0. In this situation the body will move with constant velocity, or constant speed in a straight line. A body in equilibrium though, does not move at all.
We can use the equilibrium condition, that all the forces in any direction add up to zero, to write down simultaneous equations and solve them for the forces we need to find.
Resolving vertically for the 2Kg particle: