Two straight paths are represented by the equations x – 3y = 2 an

1.	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» 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; a₁/a₂ = – ½ b₁/b₂ = – 3/6 = – ½ c₁/c₂ = 2/5 i.e., a₁/a₂ = b₁/b₂ ≠ c₁/c₂ [parallel lines] Hence, two straight paths represented by the given equations never cross each other, because they are parallel to each other.

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»

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;

a₁/a₂ = – ½

b₁/b₂ = – 3/6 = – ½

c₁/c₂ = 2/5

i.e., a₁/a₂ = b₁/b₂ ≠ c₁/c₂ [parallel lines]

Hence, two straight paths represented by the given equations never cross each other, because they are parallel to each other.