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If the system of equations $x + y - 3 = 0, (1 + k) x + (2 + k) y - 8 = 0$ and $x - (1 + k) y + (2 + k) = 0$ is consistent then the value of $' k'$ may be

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- \frac{5}{3}

\frac{3}{5}

answer is C.

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Detailed Solution

| \begin{matrix} 1 & 1 & - 3 \\ 1 + k & 2 + k & - 8 \\ 1 & - (1 + k) & (2 + k) \end{matrix} | = 0

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$\Rightarrow 1 ((k + 5) + (3 k - 5) (k + 2)) = 0$

$\Rightarrow$ $k + 5 + 3 k^{2} + 6 k - 5 k - 10 = 0$

$\Rightarrow$ $3 k^{2} + 2 k - 5 = 0$

$\Rightarrow$ $(3 k + 5) (k - 1) = 0$

$\Rightarrow$ $k = \frac{- 5}{3} (o r) 1$

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