If the pair of linear equations 4x + (k + 1)y = 15 and 7x + 8y = 16 has no solution, then the value of k is

\frac{13}{2}

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\frac{25}{7}

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\frac{15}{2}

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\frac{39}{7}

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Solution

The correct option is B $\frac{25}{7}$

Given : $4 x + (k + 1) y = 15 and 7 x + 8 y = 16$
For a pair of linear equations $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ to have no solution,
$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{4}{7} = \frac{k + 1}{8} \neq \frac{15}{16}$
$\Rightarrow 4 \times 8 = 7 (k + 1)$
$7 k = 32 - 7$
$\Rightarrow k = \frac{25}{7}$
Hence, the correct answer is option (2).

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