Question

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

• A. -1
• B. -7
• C. $\frac{1}{7}$
• D. 9

Answer 1

Answer: (B)

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