Question

How to balance
Al+NH4ClO4-->Al2O3+AlCl3+H2O+N2 using the algebraic method?

Answer 1

Give variables a,b,c,d,e,f for all reactants and products

a Al + b NH4ClO4 -> c Al2O3 + d AlCl3 + e H2O + f N2

Then make equations for all elements:

Al: a = 2c + d
N: b = 2f
H: 4b = 2e
Cl: b = 3d
O: 4b = 3c + e

There are six variables and five equations. You can give
A value for one variable. E.g b= 1 would be a good start, you can solve
Others.