Answer
$$\emptyset $$
Work Step by Step
$$\eqalign{
& \,\,\,\,\,\,{x^2} + {y^2} = 4\,\,\,\,\,\left( {\bf{1}} \right) \cr
& \,5{x^2} + 5{y^2} = 28\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }} - 5{\text{ and add both equations}} \cr
& - 5{x^2} - 5{y^2} = - 20 \cr
& \underline {\,\,\,5{x^2} + 5{y^2} = 28} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\, = 8 \cr
& {\text{The statement is false, then the system of nonlinear equations}} \cr
& {\text{has no solutions}}{\text{.}} \cr
& \cr
& {\text{Therefore, the solution set of the system is}} \cr
& \emptyset \cr} $$
