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It is proved a theorem providing necessary and sufficient conditions enablingone to map a nonlinear system of first order partial differential equations,polynomial in the derivatives, to an equivalent autonomous first order systempolynomially homogeneous in the derivatives. The result is intimately relatedto the symmetry properties of the source system, and the proof, involving theuse of the canonical variables associated to the admitted Lie point symmetries,is constructive. First order Monge-Amp\`ere systems, either with constantcoefficients or with coefficients depending on the field variables, where thetheorem can be successfully applied, are considered.

Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives