Army Group X Practice Set 3

The family of lines passing through the intersection of given lines is
(2x+3y−4)+λ+(x−5y+7)=0...(i)
This line meets X -axis (y=0) and x -intercepts −4 , so passing through thisline (−4,0) so , from Eq. (i)
(−8−4)+λ(−4+7)=0
−12+3λ−0
⇒λ=4
On putting the value of λ in Eq . (i),we get
(2x+3y−4)+4(x−5y+7)=0
6x−17y+24=0, which is the requiredequation.