Solve the following set of equations using the Gaussian method: 
Definitions:
Seborrheic Infantile Dermatitis
A common skin condition in infants causing scaly patches, usually on the scalp, known as cradle cap.
Hebra's Pityriasis
An alternative term for Pityriasis Rosea, a skin rash condition of unknown cause featuring a distinctive pattern over the body.
Allergic Dermatitis
Inflammatory skin condition triggered by an allergic reaction to substances or allergens.
Dyes
Substances used to add color to materials, from textiles to biological tissue samples for microscopic examination.
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