  We prove that the monodromy group of a reduced irreducible square system of
general polynomial equations equals the symmetric group. This is a natural
first step towards the Galois theory of general systems of polynomial
equations, because arbitrary systems split into reduced irreducible ones upon
monomial changes of variables.
  In particular, our result proves the multivariate version of the
Abel--Ruffini theorem: the classification of general systems of equations
solvable by radicals reduces to the classification of lattice polytopes of
mixed volume 4 (which we prove to be finite in every dimension). We also notice
that the monodromy of every general system of equations is either symmetric or
imprimitive, similarly to what Sottile and White conjectured in Schubert
calculus.
  The proof is based on a new result of independent importance regarding dual
defectiveness of systems of equations: the discriminant of a reduced
irreducible square system of general polynomial equations is a hypersurface
unless the system is linear up to a monomial change of variables.
