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

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Are the following pair of linear equations consistent? Justify your answer.

1. \(-3x - 4y = 12\); \(4y + 3x = 12\)

Answer:

Consistent because it satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)
Consistent because it satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
Inconsistent because it does not satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\) or \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

2. \(\frac{3}{5}x - y = \frac{1}{2}\); \(\frac{1}{5}x - 3y = \frac{1}{6}\)

Answer:

Consistent because it satifies the condition \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)
Consistent because it satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\)
Inconsistent because it does not satifies the condition \(\frac{a_1}{a_2} \neq \frac{b_1}{b_2}\) or \(\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}\)

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