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

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Asked: March 11, 20222022-03-11T11:56:37+05:30 2022-03-11T11:56:37+05:30

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The graphs of ax + by = c, dx + ey = f will be

I. parallel, if the system has no solution.

II. coincident, if the system has finite numbers of solutions.

III. intersecting, if the system has only one solution.

Which of the above statements are correct?

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Bhanu Chaudhary · Answer 1 · 2022-03-11T11:58:33+05:30

Correct Answer: Only I and III

ax + by = c and dx + ey = f

a1/a2=a/d,b1/b2=b/e,c1/c2=c/f

Because, b1/b2=c1/c2

Therefore, b/e=c/f

It represents a pair of parallel lines.

Because, a1/a2=b1/b2

Therefore, a/d=b/e

Therefore, system has unique solution and represents a pair of intersecting lines.