  A system of \ell linear equations in p unknowns Mx=b is said to have the
removal property if every set S \subseteq {1,...,n} which contains
o(n^{p-\ell}) solutions of Mx=b can be turned into a set S' containing no
solution of Mx=b, by the removal of o(n) elements. Green [GAFA 2005] proved
that a single homogenous linear equation always has the removal property and
conjectured that every set of homogenous linear equations has the removal
property. We confirm Green's conjecture by showing that every set of linear
equations (even non-homogenous) has the removal property.
