For what value of $k$ will the equations $3 x - 4 y = 5$ and $9 x - 12 y = k$ be consistent?

10

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12

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15

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18

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Solution

The correct option is C $15$
For consistency, $\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}}$
Given equations are $3 x - 4 y = 5$ and $9 x - 12 y = k$
Taking the ratios of the corresponding coefficients, we get
$\frac{9}{3} = \frac{- 12}{- 4} = \frac{k}{5}$
$\Rightarrow 3 = 3 = \frac{k}{5}$
$\Rightarrow k = 5 \times 3 = 15$

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