The graphs of \(ax+by=c\) and \(dx+ey=f\) will be:
(A) parallel, if the system has no solution.
(B) coincident, if the system has finite numbers of solutions.
(C) intersecting, if the system has only one solution.
Which of the above statements is/are correct?
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (C) and (A) only
The graph of each linear equation is a straight line, and a solution of the system is a point that lies on both lines. So the number of solutions is the number of points the two lines share.
(A) parallel, if the system has no solution. Correct. With no solution the lines share no point, so they never meet: they are parallel.
(B) coincident, if the system has finite numbers of solutions. Incorrect. Coincident lines lie one on the other and share every point, so the system has infinitely many solutions, not a finite number.
(C) intersecting, if the system has only one solution. Correct. Two lines that cross meet at one point, and that point is the only solution.