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?
Correct Answer: Only I and III
Explanation:
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.
