RO-NMO 2015 Problem 103

Find all functions $f,g:\mathbb{Q}\longrightarrow\mathbb{Q}$ that verify the relations $$\left\{\begin{matrix} f(g(x)+g(y))=f(g(x))+y g(f(x)+f(y))=g(f(x))+y\end{matrix}\right. ,$$ for all $x,y\in\mathbb{Q} .$