Two straight paths are represented by equations x-3y=2 and -2x+6y=5.Check whether the path cross each other or not.

No they will not cross each other... As we know that when a1/a2=b1/b2 is not= to c1/c2 which is the situation of parallel lines. And same is here.a1/a2=b1/b2 is not= to c1/c2 1/-2=-3/6is not =to 2/5 So they will not cross each other.