The number of common solutions for the system of linear equations $5 x + 4 y + 6 = 0$ and $10 x + 8 y + 15 = 0$ are

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None of above

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Solution

The correct option is B 0
Given linear equations are
$5 x + 4 y + 6 = 0 ⟹ a_{1} = 5, b_{1} = 4, c_{1} = 6$ and
$10 x + 8 y + 15 = 0 ⟹ a_{2} = 10, b_{2} = 8, c_{2} = 15$

Here,
$\frac{a_{1}}{a_{2}} = \frac{5}{10} = \frac{1}{2}, \frac{b_{1}}{b_{2}} = \frac{4}{8} = \frac{1}{2}, \frac{c_{1}}{c_{2}} = \frac{6}{15} = \frac{2}{5} ∴ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$

Thus, given pair of linear equations has no solution and is inconsistent.

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