Question

The paths traced by the wheels of two trains are given by equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0. Will the paths cross each other?

Answer 1

Given paths traced by the wheel of two trains are

x + 2y – 4 = 0 …(i)

2x + 4y – 12 = 0

⇒ x + 2y – 6 = 0 …(ii)

As we can see that a₁ = 1, b₁ = 2 and c₁ = – 4

and a_{2 =} 1, b₂ = 2 and c₂ = – 6

∴ Given pair of equations has no solution

Hence, two paths will not cross each other.