# Chemical equilibrium for simultaneous dissociation reactions

While calculating the adiabatic flame temperature for the following combustion reaction:

$$\ce{\Phi\, C2H6 + 3.5\,(O2 + 3.76\,N2) -> a\,CO2 + b\,CO + d\,H2O + e\,H2 + f\,O2 + g\,N2}$$

Where $\Phi$ is the equivalence ratio.

To determine the product composition ratios $a$, $b$, $d$, $e$, $f$ I need to make mass balance on $\ce{C}$, $\ce{O}$ and $\ce{H}$ and then use two $K_{p}$ (Chemical equilibrium constant) relations. Then solve this system of equation simultaneously.

My question is about the elementary reactions of dissociation I should use to apply $K_{p}$ equations, As I could have the following scenarios happening (regarding dissociation): \begin{align} \ce{CO + H2O &<=> CO2 + H2}\\ \ce{CO2 &<=> CO + $0.5$\,O2}\\ \ce{H2O &<=> H2 + $0.5$\,O2}\\ \end{align}

I only need two equations for $K_{p}$ which two should I use and why?