A pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ is inconsistent if

\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}

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\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}

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\frac{a_{1}}{a_{2}} \neq \frac{c_{1}}{c_{2}}

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\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

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Solution

The correct option is D $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
A pair of linear equations is said to be inconsistent if pair of equations has no solution and condition for no solution is
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Hence, the correct option is (D).

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