Find the equation of component lines whose combined equation is `6x^(2)+5xy-4y^(2)+7x+13y-3=0` without solving for xor y.

Explanation

Given equation of pair of straight lines is :
`6x^(2)+5xy-4y^(2)+7x+13y-3=0` (1)
Homogenous part given equations is
`6x^(2)+5xy-4y^(2)=0` (2)
or `(3x+4y)(2x-y)=0`
This represents equations of pair of straight lines parallel to the component lines of given equation .
therefore , given equation of pair of straight lines can be put as
`(3x+y+A) (2x-y+B) =0` (3)
Comparing coefficients of (1) and (3), we get
`A=-1andb=3`
Hence , the required component lines are `2x-y+3=0,3x+4y-1=0`.