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If the lines $x+3 y-9=0,4 x+b y-2=0$ and $2 x-y-4=0$ are concurrent, then $b=$
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Verified Answer
The correct answer is:
$-5$
Given lines are concurrent, then there coefficient determinant is zero.
$\begin{aligned}
&\text { So, }\left|\begin{array}{ccc}
1 & 3 & -9 \\
4 & b & -2 \\
2 & -1 & -4
\end{array}\right|=0 \\
&\Rightarrow 1(-4 b-2)-3(-16+4)-9(-4-2 b)=0 \\
&\Rightarrow-4 b-2+36+36+18 b=0 \\
&\Rightarrow 14 b+70=0 \\
&\Rightarrow b=-5
\end{aligned}$
$\begin{aligned}
&\text { So, }\left|\begin{array}{ccc}
1 & 3 & -9 \\
4 & b & -2 \\
2 & -1 & -4
\end{array}\right|=0 \\
&\Rightarrow 1(-4 b-2)-3(-16+4)-9(-4-2 b)=0 \\
&\Rightarrow-4 b-2+36+36+18 b=0 \\
&\Rightarrow 14 b+70=0 \\
&\Rightarrow b=-5
\end{aligned}$
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