The graph of ax + by = c, dx + ey = f will beI. parallel,

Home » Aptitude » Linear Equation » Question

The graph of ax + by = c, dx + ey = f will be
I. parallel, if the system has no solution.
II. coincident, if the system has finite number of solutions.
III. intersecting. if the system has only one solution.
Which of the above statements are correct ?

1. Only I and II
2. Only II and II
3. Only I and III
4. I, II and III

Correct Option: C

ax + by = c and dx + ey = f
a₁/a₂ = a/d, b₁/b₂ = b/e, c₁/c₂ = c/f
∵ b₁/b₂ ≠ c₁/c₂
∴ b/e ≠ c/f
it represent a pair of parallel lines.
∵ a₁/a₂ ≠ b₁/b₂
∴ a/d ≠ b/e
Therefore, system has unique solutions and represents a pair of intersecting lines.