Answer
$$\eqalign{
& {\text{Infinitely many solutions}}{\text{.}} \cr
& \left( {\frac{{y + 9}}{4},y} \right) \cr} $$
Work Step by Step
$$\eqalign{
& 4x\,\,\, - \,\,\,\,y\,\,\,\, = 9\,\,\,\,\,\,\,\,\,\,\left( {\bf{1}} \right) \cr
& - 8x + 2y = - 18\,\,\,\,\left( {\bf{2}} \right) \cr
& {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by 2}} \cr
& 8x\,\,\, - \,\,2\,\,y\,\,\,\, = 18\,\,\,\,\,\,\,\,\,\, \cr
& - 8x + 2y = - 18\,\,\,\, \cr
& {\text{Add both equations}} \cr
& 8x\,\,\, - \,\,2\,\,y\,\,\,\, = 18\,\,\,\,\,\,\,\,\,\, \cr
& - 8x + 2y\,\,\,\, = - 18\,\,\,\, \cr
& - - - - - - - - - - \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0 = 0\,\,\,\,\,\,\,\,\,\,\, \cr
& {\text{The result}},{\text{ }}0 = 0,{\text{ is a true statement}},{\text{ which indicates that the }} \cr
& {\text{equations are equivalent}}{\text{. Therefore,}} \cr
& {\text{The system has infinitely many solutions}}{\text{.}} \cr
& \cr
& {\text{Solve the equation }}\left( {\bf{1}} \right){\text{ for }}x \cr
& 4x - y\, = 9 \cr
& x = \frac{{y + 9}}{4} \cr
& \cr
& {\text{The solutions of the system can be written in the form of a set }} \cr
& {\text{of ordered pairs }}\left( {\frac{{y + 9}}{4},y} \right) \cr} $$
