Question

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

Answer 1

As '3' lines are concurrent $\therefore$ meet at single

pt. Hence $3y+4x=1$ if $\Rightarrow 1+5,5y+bx=3$

Pass through 1 common pt. 'A' (say).

$3y+4x=1$ & $y=x+5$ (solving zeq${}^n$)

we get $3(x+5)+4x=1\Rightarrow x=-2\&y=3$

Put $x=-2$ & $y=3$ in $5y+bx=3$

$\Rightarrow 15-2b=3\Rightarrow b=6$