Answer
$$\left\{ {\left( { - 2,2} \right)} \right\}$$
Work Step by Step
$$\eqalign{
& \frac{{3x}}{2} + \,\,\frac{y}{2}\, = - 2\,\,\, \cr
& \,\,\frac{x}{2} + \,\,\frac{y}{2}\, = 0\,\,\,\,\,\, \cr
& {\text{Clear the denominators}} \cr
& 2\left( {\frac{{3x}}{2}} \right) + \,\,2\left( {\frac{y}{2}} \right)\, = 2\left( { - 2} \right)\,\,\, \cr
& \,\,2\left( {\frac{x}{2}} \right) + \,\,2\left( {\frac{y}{2}} \right)\, = 0\,\,\,\,\,\, \cr
& \cr
& 3x + \,\,\,y = - 4\,\,\,\left( {\bf{1}} \right) \cr
& \,\,x + \,\,\,y = 0\,\,\,\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }} - 1{\text{ }} \cr
& - 3x - y = 4\,\,\,\, \cr
& \,\,\,\,x + \,\,\,y = 0\,\, \cr
& {\text{Add both equations}} \cr
& - 3x - y = 4\,\,\,\, \cr
& \,\,\,\,x + \,\,\,y = 0\,\, \cr
& - - - - - - - - - - - \cr
& - 2x\,\,\,\,\,\,\,\,\, = 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,x = - 2 \cr
& {\text{Substitute }}x = - 2{\text{ into the equation }}\left( {\bf{2}} \right) \cr
& - 2 + \,\,\,y = 0 \cr
& y = 2 \cr
& \cr
& {\text{The solution set is}} \cr
& \left\{ {\left( { - 2,2} \right)} \right\} \cr} $$
