Using simple algebraic manipulation, it can be stated that  increases or decreases monotonically within all  range, if  or  with , respectively.
When  and , the activity coefficient curve of component 1 shows a maximum and compound 2 minimum at:
Same expression can be used when  and , but in this situation the activity coefficient curve of component 1 shows a minimum and compound 2 a maximum. 
It is easily seen that when A=0 and A>0  that a maximum in the activity coefficient of compound 1 exists at x=1/3. Obvious, the activity coefficient of compound 2 goes at this concentration through a minimum as a result of the Gibbs-Duhem rule.
The binary system Chloroform(1)-Methanol(2) is an example of a system that shows a maximum in the activity coefficient of Chloroform. The parameters for a description at 20 °C are A=0.6298 and A=1.9522. This gives a minimum in the activity of Chloroform at  x=0.17.
In general, for the case A=A=A, the larger parameter A, the more the binary systems deviates from Raoult's law; i.e. ideal solubility. When A>2 the system starts to demix in two liquids at 50/50 composition; i.e. plait point is at 50 mol%. Since:
For asymmetric binary systems, A≠A, the liquid-liquid separation always occurs for 
Or equivalently:
The plait point is not located at 50 mol%. It depends on the ratio of the limiting activity coefficients.