Question

If $3y+4x=1,y=x+5$ and $5y+bx=3$ are concurrent, then the value of '$b$' is

• A. 1
• B. 3
• C. 6
• D. 0

Answer 1

Answer: (C)

6

The equations of the straight lines are $3y+4x=1$ ........(i)

$y=x+5$ .........(ii)

$5y+bx=3$ .......(iii)and they are concurrent.

So, the point of intersection of line (i) and (ii) will satisfy the equation (iii).

Now multiplying equation (ii) by $3$ and subtractingd from equation (i), we get

$7x=-14$

$\Rightarrow x=-2$

Substituting $x=-2$ in equation (i), we have

$y=-2+5=3$

therefore, the point of intersection is $(-2,3)$

This point satisfies equation (iii)

Therefore, substituting these values of $x$ and $y$ in equation (iii, we get

$5\times 3+b\times (-2)=3$

$\Rightarrow b=6$