SUMMARY
A hyperbolic system with a convex extension is usually transformed in the symmetric form by taking the components of the main field as independent variables. However, the symmetric form can be obtained also in the original independent variables, which may have more physical meaning, by multiplying the system on the left by a suitable matrix P. Here the two methods are compared, showing also how to find the matrix P . The experience gained in this way, allows us to find also a new method to treat the systems with algebraic and differential constraints, without losing manifest covariance. The particular case of Lagrangian systems is also considered.