Find all solutions to the following system of equations.

$$\left\lbrace \begin{array}{rcrcr} x^2 &+ &2 y^2 &=& 6 \cr 2 x^2 & - & 2 y & = & 17 \end{array} \right.$$

Enter the solutions as a list of ordered pairs (e.g., (1,5), (-2,6)). If there are no solutions, enter None.

Solutions: