We have a linear equation 2x + 3y – 8 = 0. Write another linear equa

1.	We have a linear equation 2x + 3y – 8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersect¬ing lines. Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.
Answer» i) Given: 2x + 3y – 8 = 0 The lines are intersecting lines. Let the other linear equation be ax + by + c = 0 ∴ a₁/a₂ ≠ b₁/b₂; we have to choose appropriate values satisfying the condition above. Thus the other equation may be 3x + 5y – 6 =0 ii) Parallel line a₁/a₂ = b₁/b₂ ≠ c₁/c₂ ⇒ 2x + 3y – 8 = 0 ⇒ 4x + 6y – 10 = 0 iii) Coincident lines a1/a2 = b1/b2 = c1/c2 ⇒ 2x + 3y – 8 = 0 ⇒ 8x + 12y – 32 = 0

We have a linear equation 2x + 3y – 8 = 0. Write another linear equation in two variables such that the geometrical representation of the pair so formed is intersect¬ing lines. Now, write two more linear equations so that one forms a pair of parallel lines and the second forms coincident line with the given equation.

Answer»

i) Given: 2x + 3y – 8 = 0

The lines are intersecting lines.

Let the other linear equation be ax + by + c = 0

∴ a₁/a₂ ≠ b₁/b₂; we have to choose appropriate values satisfying the condition above.

Thus the other equation may be 3x + 5y – 6 =0

ii) Parallel line a₁/a₂ = b₁/b₂ ≠ c₁/c₂

⇒ 2x + 3y – 8 = 0

⇒ 4x + 6y – 10 = 0

iii) Coincident lines a1/a2 = b1/b2 = c1/c2

⇒ 2x + 3y – 8 = 0

⇒ 8x + 12y – 32 = 0