Check to see if two variables are dependent or independent. If two symbols appear in the same equation, they are dependent. Variables that do not appear in the same equation can be dependent or independent. For example, say you have two equations with variables A and B in one equation and B and C in the other. Changing A changes B according to one equation and changing B changes C according to the other equation, therefore changing A changes C because A and C are dependent. These "chains of dependency" determine dependency in a system of equations.
Look for direct relationships between two variables: when one variable increases, the other increases and when one variable decreases, the other decreases. This happens when the variables are on opposite sides of the = sign. For example, in the equation A = kB, where A and B are variables and k is a constant, A and B rise and fall together. A real world example is the ideal gas law PV = rT, which describes the relationships between pressure, volume and temperature in a gas. Temperature relates directly to both pressure and volume. If temperature goes up, either pressure or volume must go up as well.
Find an inverse relationship where one variable increases and another decreases. This happens when the variables are on the same side of the = sign. An example is found in the ideal gas law PV = rT. Assuming that the temperature stays constant, whenever the volume goes up, the pressure goes down, and whenever the volume goes down, the pressure goes up.