A system initially charged with \(3 \mathrm{~mol} \mathrm{CH}_{4}\) and \(4 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) is undergoing the following reaction:

\[ \begin{align*} \mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}+3 \mathrm{H}_{2} \tag{A}\\ \mathrm{CH}_{4}+2 \mathrm{H}_{2} \mathrm{O} & \rightarrow \mathrm{CO}_{2}+4 \mathrm{H}_{2} \tag{B} \end{align*} \]

Derive the expression for the mole fractions of the components in terms of extent of the reactions.