Question

If lines $4x+3y=1,y=x+5\mathrm{and}5y+bx=3$ are concurrent, then $b$ equals:

• A. $1$
• B. $3$
• C. $6$
• D. $0$

Answer 1

The correct option is C

$6$

Explanation for the correct option.

Step 1: Find the value of $x\mathrm{and}y$.

$$\begin{gathered} 4x+3y=1.....\left(1\right) \\ y=x+5.......\left(2\right) \end{gathered}$$

Substituitng the value of $y$ from $\left(2\right)$in $\left(1\right)$, we get

$\begin{array}{rcl}4x+3\left(x+5\right)& =& 1\\ & \Rightarrow & 4x+3x+15=1\\ \Rightarrow 7x& =& -14\\ \Rightarrow x& =& -2\end{array}$

By substituting the value of $x$ in $\left(2\right)$, we get

$y=3$

Step 2: Find the value of $b$.

The given lines are concurrent, it means they pass through same points. So, $\left(-2,3\right)$ should satisfy the equation $5y+bx=3$.

$$\begin{gathered} \Rightarrow 5\left(3\right)+b\left(-2\right)=3 \\ \Rightarrow b=\frac{3-15}{-2} \\ =6 \end{gathered}$$

Hence, option C is correct.