9000020905

Find the condition on the parameter $c\in \mathbb{R}$ which ensures that the following system has a unique solution in $\mathbb{R}\times \mathbb{R}$. $$\begin{array}{rlrlrlrlrlr}& x^2& +& y^2& =2& & & & & & \\ & x& +& c& =y& & & & & & \end{array}$$