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You can write a series of simultaneous equations, one for each type of atom. For example, in the reaction to produce water: aH2 + bO2 --> cH2O, you want to find out the coefficients a, b, and c, so you write the following equations:

For atom H: 2a = 2c

For atom O: 2b = c

Note that you only have two equations, for three unknowns. This is common in this case; after all, you won't find out, in absolute terms, how much of each reactant you need; only the relationship between them. Solving the equations, you get the relative amounts of the substances.

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