If the lines `3y+4x=1, y=x+5` and `5y+bx=3` are concurrent then `b=`

Options

A. 1
B. 3
C. 6
D. 0

Answer

C

Explanation

The equation of given lines are
`3y+4x=1" "...(i)`
`y=x+5" "...(ii)`
`and 5y+bx=3" "...(iii)`
On solving Eqs. (i) and (ii), we get x = -2 and y = 3
If thesee lines are concurrent, then these values must satisfy the third equation
` 15 -2 b = 3 rArr 2b = 12 rArr b = 6`
ALTERNATE SOLUTION : Given equation of lines are
`3y+4x-1=0`
`x+5-y=0 and`
`bx+5y-3=0`
Since, the given lines are concurrent
`therefore` The value of determinant made by coeff of equations is 0.
`ie, |{:(4,3,-1),(1,-1,5),(b,5,-3):}|=0`
`rArr 4(3-25)-3(-3-5b)-1(5+b)=0`
`rArr -88+4+14b=0`
`rArr -84 = -14b`
`rArr b = 6`.