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

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1. Is it true to say that the pair of equations \(-x + 2y + 2 = 0\) and \(\frac{1}{2}x - \frac{1}{4}y - 1 = 0\) has a unique solution? Justify your answer.

Answer:

The pair of equations has a unique solution.

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

2. Do the equations \(4x + 3y - 1 = 5\) and \(12x + 9y = 15\) represent a pair of coincident lines? Justify your answer.

Answer:

The pair of equations \(4x + 3y - 1 = 5\) and \(12x + 9y = 15\) represent coincident lines.

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

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19. Exemplar problems IX

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