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

The given system is consistent. Therefore,Δ=11−12−1−c−b3b−c=0or   c+bc−6b+b+2c+3bc=0or   3c+4bc−5b=0or   c=5b4b+3Now, c < 1⇒ 5b4b+3<1or   5b4b+3−1<0or   b−34b+3<0⇒ b∈−34,3