Obtain the equations of the line passing through the intersection of lines `4x-3y-1=0\ a n d\ 2x-5y+3=0` and equally inclined to the axes.

Explanation

The equation of any line through the intersection of the given lines is

`(4x−3y−1)+λ(2x−5y+3)=0`
or
`x(2λ+4)−y(5λ+3)+3λ−1=0 ........(i)`

Let `m` be the slope of this line
Then `m = (2λ+4​)/(5λ+3)`

As the line is equally inclined with the axes
therefore

`m = tan(45)^∘` or
`m=tan(135)^∘`

`m=±1`

`(2λ+4​)/(5λ+3)=±1`

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