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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