I recently discovered that I could solve a chemical reaction using a linear system. So I thought I would try something simple like the combustion of methane.
w are the moles of each molecule
x $CH_4$ + y $O_2$ = z $H_2$O + w C$O_2$
the linear system for this would be:
x = w 2y = z + 2w 4x = 2z
I got as far as
y = z and
y = 2w but without any constants, I am stumped. Can anyone help me? I was assuming that elimination and substitution would suffice, but I must be wrong.