Question

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

Answer 1

Given linear equations are

x – 3y – 2 = 0  ......(i)

–2x + 6y – 5 = 0   ......(ii)

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

a₁ = 1, b₁ = –3, c₁ = – 2

a₂ = –2, b₂ = 6, c₂ = – 5

`a_1/a_2 = 1/(-2)`

`b_1/b_2 = (-3)/6 = -1/2`

`c_1/c_2 = 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.