Find the equation of a line which passes through the point `(1,1)` and through the intersection of lines `x+y-1=0` and `3x+2y+1=0`.

Explanation

Let the equation of a line through the intersection of `x+y-1=0` and `3x+2y+1=0` be
`(x+y-1)+lambda(3x+2y+1)=0`……..`(1)`
This line passes through the point `(1,1)`
`:. (1+1-1)+lambda(3+2+1)=0`
`implies lambda=-(1)/(6)`
From eq. `(1)`, equation of requried line is
`(x+y-1)-(1)/(6)(3x+2y+1)=0`
`implies 6x+6y-6-3x-2y-1=0`
`implies 3x+4y-7=0`