For  $l\in R$ , the equation $(2l-3)x^2+2lxy-y^2=0$ represents a pair of lines

The equation $(2l-3)x^2+2lxy-y^2=0$  will represent a pair of real and distinct lines, if
     $l^2(2l-3)(-1)>0$             $[\because h^2>ab]$
 $$\begin{gathered} \Rightarrow l^2+2l-3>0 \\ \Rightarrow (l+3)(l-1)>0 \\ \therefore l\in R-(-3,1) \end{gathered}$$