2010006704

Determine all the values of the parameter $c\in \mathbb{R}$ so that the following system has two solutions in $\mathbb{R}\times \mathbb{R}$. $$\begin{array}{rlrlrlrlrlr}& x^2& +& 2y^2& =6& & & & & & \\ & x& +& y& =c& & & & & & \end{array}$$