Answer
$$\left\{ {\left( {4,6} \right)} \right\}$$
Work Step by Step
$$\eqalign{
& \frac{x}{2} + \,\,\,\,\,\,\,\frac{y}{3}\, = 4\,\,\,\,\, \cr
& \frac{{3x}}{2} + \frac{{3y}}{2} = 15\,\, \cr
& {\text{Clear the denominators}} \cr
& 6\left( {\frac{x}{2}} \right) + \,\,\,\,\,\,\,6\left( {\frac{y}{3}\,} \right) = 6\left( 4 \right)\,\,\,\,\, \cr
& 2\left( {\frac{{3x}}{2}} \right) + \,\,\,2\left( {\frac{{3y}}{2}} \right) = 2\left( {15} \right)\,\, \cr
& \cr
& 3x + \,\,\,2y = 24\,\,\,\,\,\left( {\bf{1}} \right) \cr
& 3x + \,\,\,3y = 30\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }} - 1{\text{ }} \cr
& - 3x - \,2y = - 24\,\,\,\, \cr
& \,\,3x + \,\,\,3y = 30\,\, \cr
& {\text{Add both equations}} \cr
& - 3x - \,2y = - 24\,\,\,\, \cr
& \,\,3x + \,\,\,3y = 30\,\, \cr
& - - - - - - - - - - - \cr
& 0x\,\,\,\,\, + y\,\,\, = 6 \cr
& y = 6 \cr
& {\text{Substitute }}y = 6{\text{ into the equation }}\left( {\bf{1}} \right) \cr
& 3x + \,\,\,2\left( 6 \right) = 24 \cr
& 3x + \,\,12 = 24 \cr
& 3x = \,\,12 \cr
& x = 4 \cr
& \cr
& {\text{The solution set is}} \cr
& \left\{ {\left( {4,6} \right)} \right\} \cr} $$