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The value of $k$ such that the lines $2 x-3 y+k=0, \quad 3 x-4 y-13=0 \quad$ and $8 x-11 y-33=0$ are concurrent, is
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Verified Answer
The correct answer is:
$-7$
Since, the lines
$$
\begin{aligned}
& 2 x-3 y+k=0,3 x-4 y-13=0 \\
& \text { and } \quad 8 x-11 y-33=0 \\
& \text { are concurrent } \\
& \therefore \quad\left|\begin{array}{ccc}
2 & -3 & k \\
3 & -4 & -13 \\
8 & -11 & -33
\end{array}\right|=0 \\
& \Rightarrow \quad 2(132-143)+3(-99+104) \\
& +k(-33+32)=0 \\
& \Rightarrow \quad-22+15-k=0 \\
& \Rightarrow \quad k=-7 \\
&
\end{aligned}
$$
$$
\begin{aligned}
& 2 x-3 y+k=0,3 x-4 y-13=0 \\
& \text { and } \quad 8 x-11 y-33=0 \\
& \text { are concurrent } \\
& \therefore \quad\left|\begin{array}{ccc}
2 & -3 & k \\
3 & -4 & -13 \\
8 & -11 & -33
\end{array}\right|=0 \\
& \Rightarrow \quad 2(132-143)+3(-99+104) \\
& +k(-33+32)=0 \\
& \Rightarrow \quad-22+15-k=0 \\
& \Rightarrow \quad k=-7 \\
&
\end{aligned}
$$
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