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

Question

Aicharya · Accepted Answer

For concurrency of 3 lines the determinant of coefficients of equations should be 0 . i.e. $\left|\begin{array}{ccc}3 & -4 & -13 \ 8 & -11 & -33 \ 2 & -3 & \lambda\end{array}ight|=0$ $\Rightarrow 3(-11 \lambda-99)+4(8 \lambda+66)-13(-24+22)=0$ $\Rightarrow-33 \lambda-297+32 \lambda+264+312-286=0$ $\Rightarrow-\lambda-583+576=0 \Rightarrow \lambda=-7$

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

Solution