I'm trying to balance a complex chemical reaction of decomposition of an organic material. I tried using Matlab to sole the set of equations I got, But the problem I get and where I think I'm missing up is that the reaction has 11 variables and once I put it into equations, I only get 4 equations as below:
The reaction : $$C_{40}H_{65}O_{25}N\rightarrow CO+CO_2+CH_4+HCN+NH_3+H_2+N_2+N_2O+NO_2+NO$$
Adding Variables [X] : $$X_0C_{40}H_{65}O_{25}N\to X_1CO+X_2CH_4+X_3H2+X_4NH_3+X_5HCN+X_6CO_2+X_7N_2+X_8N_2O+X_9NO+X_{10}NO_2$$
The goal is to find the values for $X$ coefficients using metrics in MATLAB in the form of $Ax=b$
The linear equations from the reaction: \begin{align} 40X_0-X_1-X_2-X_5-X_6&=0\\ 65X_0-4X_2-2X_3-3X_4-X_5&=0\\ 25X_0-X_1-2X_6-X8-X_9-2X_{10}&=0\\ X_0-X_4-X_5-2X7-2X8-X_9-X_{10}&=0 \end{align}
I tried solving in Matlab, but I didn't get any values that made sense, where am I missing up ?!