Exemplar problems XIII — task. Mathematics CBSE, Class 10.

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Do the following equations represent a pair of coincident lines? Justify your answer.

1. \(-2x - 3y = 1\); \(6y + 4x = -2\)

Answer:

Yes, because it satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)
No, because it does not satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
Yes, because it satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
No, because it does not satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)

2. \(\frac{x}{2} + y + \frac{2}{5} = 0\); \(4x + 8y + \frac{5}{16} = 0\)

Answer:

Yes, because it satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
No, because it does not satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
No, because it does not satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)
Yes, because it satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)

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