Answer
$$\emptyset ;{\text{Inconsistent System }}$$
Work Step by Step
$$\eqalign{
& 5x - 5y - 3\,\, = 0\,\,\,\,\left( {\bf{1}} \right) \cr
& x - y - 12\,\,\,\, = 0\,\,\,\,\left( {\bf{2}} \right) \cr
& \cr
& {\text{Multiply the equation }}\left( {\bf{2}} \right){\text{ by }}5 \cr
& 5x - 5y - 3\,\,\,\,\, = 0\,\,\, \cr
& 5x - 5y - 60\,\,\, = 0\,\,\,\, \cr
& {\text{Add both equations}} \cr
& 5x - 5y - 3\,\,\,\,\, = 0 \cr
& \underline {5x - 5y - 60\,\, = 0} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 63 = 0\,\,\,\,\,\,\,\,\,\,\, \cr
& {\text{The result}},{\text{ }} - 63 = 0,{\text{ is a false statement}},{\text{ which indicates that}} \cr
& {\text{The system is inconsistent and has no solutions}}{\text{.}} \cr} $$
