Answer
$$\emptyset $$
Work Step by Step
$$\eqalign{
& \,\,\,2{x^2} + 2{y^2} = 20\,\,\,\,\,\left( {\bf{1}} \right) \cr
& \,\,\,4{x^2} + 4{y^2} = 30\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }} - 2{\text{ and add both equations}} \cr
& \,\, - 4{x^2} - 4{y^2} = 20 \cr
& \underline {\,\,\,\,\,\,4{x^2} + 4{y^2} = 30} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\, = 50 \cr
& {\text{The statement is false, then the system of nonlinear equations}} \cr
& {\text{has no solutions}}{\text{.}} \cr
& \cr
& {\text{Therefore, the solution set of the system is}} \cr
& \emptyset \cr} $$
