If the lines $4 x+3 y-1=0, x-y+5=0$ and $k x+5 y-3=0$ are concurrent then $k$ is equal to

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Aicharya · Accepted Answer

We have, $ \begin{array}{r} 4 x+3 y-1=0 \ x-y+5=0 \ k x+5 y-3=0 \end{array} $ are concurrent lines : $ \begin{array}{rrrr} & & \left|\begin{array}{rrr} 4 & 3 & -1 \ 1 & -1 & 5 \ k & 5 & -3 \end{array}ight|=0 \ \Rightarrow & & 4(3-25)-3(-3-5 k)-1(5+k)=0 \ \Rightarrow & & -88+9+15 k-5-k=0 \ & 14 k=84 \Rightarrow k & =6 \end{array} $

If the lines $4 x+3 y-1=0, x-y+5=0$ and $k x+5 y-3=0$ are concurrent then $k$ is equal to

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