Equation of line in Straight lines

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Question

The value of $k$ for which the lines $2 x - 3 y + k = 0$ $3 x - 4 y - 13 = 0$ and $8 x - 11 y - 33 = 0$ are concurrent, is

Moderate

Solution

If given lines are concurrent, then
$|\begin{array}{lr} 2 - 3 k \\ 3 - 4 - 13 \\ 8 - 11 - 33 \end{array}| = 0 \Rightarrow - 22 + 15 - k = 0 \Rightarrow k = - 7$

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