Find the equation of a line which passes through the intersection of lines `2x+y-1=0` and `x-3y+1=0` and parallel to `x`-axis.

Explanation

Equation of a line, passing through the intersection of lines `2x+y-1=0` and `x-3y+1=0` be
`(2x+y-1)+lambda(x-3y+1)=0`
`implies x(2+lambda)+y(1-3lambda)+lambda-1=0`…..`(1)`
This line will be parallel to `X`-axis if
`"Coefficient of" x=0`
`2+lambda=0`
`implies lambda=-2`
Put `lambda=-2` in eq. `(1)`
`0+y(1+6)+(-2-1)=0`
`implies 7y-3=0`