The lines represented by the equation $x^2-y^2-x+3y-2=0are$

:  Let the line $x^2-y^2-x+3y-2=0represent$

The lines

$\begin{array}{l}x+y+l=0,x-y+k=0\\ \therefore x^2-y^2-x+3y-2=\left(x+y+l\right)\left(x-y+k\right)\\ =x^2-y^2+x\left(k+l\right)+y\left(k-l\right)+lk\end{array}$

Comparing on both sides

$\begin{array}{l}k+l=-1---\left(i\right)k-l=3---\left(ii\right)\\ \left(i\right)+\left(ii\right)\Rightarrow 2k=2\\ k=1\\ From\left(i\right)1+l=-1\\ l=-2\end{array}$

The lines are x+y-2=0,  x-y+1=0