  We study the De Giorgi type conjecture, that is, one dimensional symmetry
problem for entire solutions of an two components elliptic system in
$\mathbb{R}^n$, for all $n\geq 2$. We prove that, if a solution $(u,v)$ has a
linear growth at infinity, then it is one dimensional, that is, depending only
on one variable. The main ingredient is an improvement of flatness estimate,
which is achieved by the harmonic approximation technique adapted in the
singularly perturbed situation.
