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

Explanation

Two straight paths are represented by the equations x - 3y = 2 and -2x + 6y = 5.
For the paths to cross each other i.e., to intersect each other, we must have `(a_(1))/(a_(2)) ne (b_(1))/(b_(2))`.
Now, `(a_(1))/(a_(2)) = (1)/(-2) = (-1)/(2)` and `(b_(1))/(b_(2)) = (-3)/(6) = (-1)/(2)`
`therefore (a_(1))/(a_(2)) = (b_(1))/(b_(2))`
Hence, the two straight paths do not cross each other.