A typical chemical formula for aerobic growth of a microorganisms is

$C_2{H}_{5}OH+a{O}_2+bN{H}_{3}cC{H}_{1\mathrm{.}7}{H}_{0\mathrm{.}15}{O}_{0\mathrm{.}4}+d{H}_{2}O+eC{O}_2$

where term $C{H}_{1\mathrm{.}7}{H}_{0\mathrm{.}15}{O}_{0\mathrm{.}4}$ represents metabolism of the microorganism. The ratio of moles of $C{O}_2$ produced per mole of $O_2$ consumed is called the respiratory quotient, $RQ,$which can be determined experimentally. Given this ratio we have $4$ constants, a$-$d that are unknown. We can perform a mass balance on each of the four key elements

Carbon: $,2=c+(RQ)a$

Hydrogen: $6+3b=1\mathrm{.}7c+2d$

Oxygen: $,1+2a=0\mathrm{.}4c+d+2(RQ)a$

Nitrogen: $b=0\mathrm{.}15c$

Let $RQ=0\mathrm{.}8$ and then find the vector $[a$ b $c$ d$]$ using Gauss Elimination Method in MATLAB