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 $a \mathrm{Fe}_{2} \mathrm{O}_{3}+b \mathrm{Al} \rightarrow c \mathrm{Al}_{2} \mathrm{O}_{3}+$ $10 \mathrm{Fe}$ . In other words, solve this system:
Fe: $\quad 2 a+0 b=10$
O: $\quad 3 a+0 b=3 c$
Al: $\quad 0 a+b=2 c$