Question

If the lines $3x+4y+1=0,5x+\lambda y+3=0$ and $2x+y-1=0$ are concurrent, then $\lambda$ is equal to:

• A. $-8$
• B. $8$
• C. $4$
• D. $-4$

Answer 1

The correct option is B

$8$

Explanation for correct option

Given lines $3x+4y+1=0,5x+\lambda y+3=0$ and $2x+y-1=0$ are concurrent

For the lines to be concurrent their determinant should be zero.

So,

$\left|\begin{array}{ccc}3& 4& 1\\ 5& \lambda & 3\\ 2& 1& -1\end{array}\right|=0$

Solving, $3(-\lambda -3)-4(-5-6)+1(5-2\lambda )=0$

$$\begin{gathered} \Rightarrow -3\lambda -9+44+5-2\lambda =0 \\ \Rightarrow -5\lambda +40=0 \\ \Rightarrow \lambda =\frac{-40}{-5} \\ \Rightarrow \lambda =8 \end{gathered}$$

Therefore, option (B) i.e. $8$ is the correct answer.