For a binary system, the influence of composition on property \(M\) can be represented by

\[ M=x_{1} M_{1}+x_{2} M_{2}+A x_{1} x_{2} \]

where \(M_{1}\) and \(M_{2}\) are the values of \(M\) for pure chemical species 1 and 2 respectively, and \(A\) is a parameter independent of composition. Develop expressions for \(\bar{M}_{1}\) and \(\bar{M}_{2}\).