The equations λx – y =2, 2x – 3y = –λ, 3x – 2y = –1 are consistent for

$\begin{vmatrix}λ&-1&-2\\2&-3&λ\\3&-2&1\end{vmatrix}=0$

$⇒λ(–3 + 2λ) + 1 (2 – 3λ) – 2(–4 + 9) + 0$

$⇒ 2λ^2 – 6λ – 8 = 0 ⇒ λ^2 – 3λ – 4 = 0$

$⇒(λ – 4) (λ + 1) = 0$  $∴ λ = –1, 4$