Determine the Coefficients $a, b$ , And $c$ Which Balance the Chemical Equation

Short Answer

Determine the coefficients $a, b$ , and $c$ which balance the chemical equation $a \mathrm{C}_{4} \mathrm{H}_{10}+13 \mathrm{O}_{2} \rightarrow b \mathrm{H}_{2} \mathrm{O}+$ $c \mathrm{CO}_{2}$ . In other words, solve this system:
C: $\quad 4 a=0 b+c$
$\mathrm{H}: \quad 10 a=2 b+0 c$
O: $\quad 26=b+2 c$