Given linear equations are
`x-3y-2=0 " " ...(i)`
and `-2x+6y-5=0" " ...(ii)`
On comparing both the equations with `ax+by+c=0`, we get
`a_(1)=1,b_(1)=-3`
and `c_(1)=-2" " `[from Eq.(i)]
`a_(2)=-2,b_(2)=6`
and `c_(2)=-5" " `[from Eq.(ii)]
Here, `" " (a_(1))/(a_(2))=(1)/(-2)`
`(b_(1))/(b_(2))=(-3)/(6)=-(1)/(2)` and `(c_(1))/(c_(2))=(-2)/(-5)=(2)/(5)`
i.e., `" " (a_(1))/(a_(2))=(b_(1))/(b_(2))!=(c_(1))/(c_(2))" "` [parallel lines]
Hence, two straight paths represented by the given equation never cross each other, because they are parallel to each other.
