Answer
$$\emptyset ;{\text{Inconsistent System }}$$
Work Step by Step
$$\eqalign{
& \,\,2x - 6y\,\,\, = 0\,\,\,\,\,\,\left( {\bf{1}} \right)\,\, \cr
& - 7x + 21y\, = 10\,\,\,\left( {\bf{2}} \right)\, \cr
& \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }}7{\text{ and the equation }}\left( {\bf{2}} \right){\text{ by 2}} \cr
& \,\,\,14x - 42y\,\,\, = 0 \cr
& - 14x + 42y\, = 20 \cr
& {\text{Add both equations}} \cr
& \,\,\,14x - 42y\,\,\, = 0 \cr
& \underline { - 14x + 42y\,\,\, = 20} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 = 20\,\,\,\,\,\,\,\,\,\,\, \cr
& {\text{The result}},{\text{ }}0 = 20,{\text{ is a false statement}},{\text{ which indicates that}} \cr
& {\text{The system is inconsistent and has no solutions}}{\text{.}} \cr} $$
