• 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?

    A) Only I and II

      B) Only ll and Ill

    C) Only I and III

      D) I, II and Ill

    Correct Answer:
    C) Only I and III

    Description for Correct answer

    ax + by = c and dx + ey = f

    \( \Large \frac{a_{1}}{a_{2}}=\frac{a}{d}, \frac{b_{1}}{b_{2}}=\frac{b}{e}, \frac{c_{1}}{c_{2}}=\frac{c}{f} \)

    Because, \( \Large \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} \)

    Therefore, \( \Large \frac{b}{e} = \frac{c}{f} \)

    It represents a pair of parallel lines.

    Because, \( \Large \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \)

    Therefore, \( \Large \frac{a}{d} = \frac{b}{e}\)

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


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