The values of λ  for which the system of equations x+y−3=0,1+λx+2+λy−8,x−1+λy+2+λ=0  is consistent are

The given system of equations will be consistent if Δ=11−31+λ2+λ−81−(1+λ)2+λ=0 Applying C2→C2−C1 and C3→C3+3C1, we get Δ=1001+λ1−5+3λ1−2−λ5+λ=0⇒(5+λ)+(2+λ)(3λ−5)=0⇒5+λ+6λ−10+3λ2−5λ=0⇒3λ2+2λ−5=0⇒(3λ+5)(λ−1)=0⇒λ=−5/3 or λ=1