If `c<1` and the system of equations `x+y-1=0,2x-y-c=0,and -bx+3b y-c=0` is consistent, then the possible real values of `b` are

Options

A. `b in (-3(3)/(4))`
B. ` b in (-(3)/(2) ,4)`
C. `b in (-(3)/(4),3)`
D. none of these

Answer

C

Explanation

the given system is consistent . Therefore
`Delta =|{:(1,,1,,-1),(2,,-1,,-c),(-b,,3b,,-c):}|=0`
`" or " c+bc -6b +b+ 2c+ 3bc=0`
`" or " 3c+4bc-5b=0`
`" or " 3c+ 4bc -5b =0`
`" or " c=(5b)/(4b+3)`
Now `c lt 1`
`rArr (5 b)/(4b+3) lt 1 `
`" or " .(5b)/(4b +3) -1 lt 0`
`rArr b in (-(3)/(4),3)`