Simultaneous equations:

Let us select the wavelengths λ₁ and λ ₂   on these two spectra. The molar absorptivity of spectra 1 and 2 can be found out by taking known amounts of the substance and recording their absorbance value. Let these values be (ε₁ ) λ₁ , (ε ₂ ) λ₁ , (ε₁ ) λ₂ , and (ε ) λ₂. If the absorbance of the solution at the wavelength λ₁ and λ₂ are Aλ₁ and   Aλ₂ respectively then we can write, for 1 cm path,

A_λ1  = C₁ (ε₁ ) λ₁+ C₂ (ε ₂ ) λ₁

A_λ2   = C₁ (ε₁ )λ₂+ C₂ (ε ₂ )λ₂

The above two simultaneous equations could be solved for C₁ and C₂. The expressions are found to be.

C_{1 =} A_λ1 (ε ₂ ) _λ2- A_λ2 (ε ₂ ) _λ1/(ε₁ ) _λ1 (ε ₂ ) _λ2- (ε ₂ ) _λ1 (ε₁ ) _λ2

C₂  = A_λ2  - (ε₁ ) λ₂ C₁/(ε )_λ2