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

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1. Do the following pair of linear equations have no solution? Justify your answer.

\(3x + y - 3 = 0\); \(2x + \frac{2}{3}y = 2\)

Answer:

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 \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)
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 \(\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

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

\(3x + \frac{1}{7}y = 3\); \(7x + 3y = 7\)

Answer:

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 \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
Yes, because it satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)

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