Two straight paths are represented by the equations and Check whether the paths cross each other or not.

Given linear equations are

x - 3y - 2 = 0 …(i)

and -2x + 6y - 5 = 0 …(ii)

On comparing with ax + by c=0, we get

Here, a_{1} =1, b_{1} =-3, c_{1} =- 2;

And a_{2} = -2, b_{2} =6, c_{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 equations never cross each other, because they are parallel to each other.

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