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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?

 A) Only I and II B) Only ll and Ill C) Only I and III D) I, II and Ill

 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.

Part of solved Linear Equations questions and answers : >> Aptitude >> Linear Equations

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