Answer
$$\left\{ {\left( {2, - 3} \right)} \right\}$$
Work Step by Step
$$\eqalign{
& 5x + 4y\,\,\,\, + \,\,\,\,2 = 0\,\,\left( {\bf{1}} \right) \cr
& 4x - 5y - \,\,\,\,23 = 0\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by 5 and the equation }}\left( {\bf{2}} \right){\text{ by 4}} \cr
& 25x + 20y\,\,\,\, + \,\,\,\,10 = 0\,\, \cr
& 16x - 20y\,\,\,\,\,\, - 92 = 0\,\, \cr
& {\text{Add both equations}} \cr
& 25x + 20y\,\,\,\, + \,\,\,\,10 = 0\,\, \cr
& 16x - 20y\,\,\,\,\,\, - 92 = 0\,\, \cr
& - - - - - - - - - - - \cr
& 41x + 0 - 82 = 0 \cr
& x = \frac{{82}}{{41}} \cr
& x = 2 \cr
& {\text{Substitute }}x = 2{\text{ into the equation }}\left( {\bf{1}} \right) \cr
& 5\left( 2 \right) + 4y\,\,\,\, + \,\,\,\,2 = 0 \cr
& 4y = - 12 \cr
& y = - 3 \cr
& \cr
& {\text{The solution set is}} \cr
& \left\{ {\left( {2, - 3} \right)} \right\} \cr} $$
