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

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

1. \(2ax + by = a\); \(4ax + 2by - 2a = 0\); \(a, b \neq 0\)

Answer:

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

2. \(x + 3y = 11\); \(2(2x + 6y) = 22\)

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

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