Question

If the lines $x+3y-9=0,4x+by-2=0$ and $2x-y-4=0$ are concurrent, then $b$ is equal to.

• A. $-5$
• B. $5$
• C. $1$
• D. $0$

Answer 1

The correct option is A

$-5$

Explanation for the correct option:

Find the value of $b$.

In the question, the lines $x+3y-9=0,4x+by-2=0$ and $2x-y-4=0$ are given.

We know that if the lines $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ and $a_{3}x+b_{3}y+c_3=0$ are concurrent , then $\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|=0$.

So,

$$\begin{gathered} \left|\begin{array}{ccc}1& 3& -9\\ 4& b& -2\\ 2& -1& -4\end{array}\right|=0 \\ \Rightarrow 1(-4b-2)-3(-16+4)-9(-4-2b)=0 \\ \Rightarrow -4b-2-3(-12)+36+18b=0 \\ \Rightarrow 70+14b=0 \\ \Rightarrow b=-5 \end{gathered}$$

Therefore, the value of $b$ is $-5$.

Hence, option (A) is the correct answer.