Question

If the lines `3y+4x=1, y=x+5` and `5y+bx=3` are concurrent the n `b=`
A. 1
B. 3
C. 6
D. `1/2`

Answer 1

Correct Answer - C
Given lines, `3y+4x=1 implies 4x+3y-1=0`
`y=x+5 implies x-y+5=0`
`5y+bx=3 implies bx+5y-3=0`
Since, these lines are concurrent,
`|(4,3,-1),(1,-1,5),(b,5,-3)|=0`
`implies 4(3-25)-3(-3-5b)-1 (5+b)=0`
`implies 4(-22)+9+15b-5-b=0`
`implies -88+4+14b=0`
`implies -84+14b=0`
`implies b=6`