Question

For which value(s) of λ, do the pair of linear equations λx + y = \lambda ^{2} and x + λy = 1 have

(i) no solution?

(ii) infinitely many solutions?

(iii) a unique solution?

Answer 1

(i) λ = -1

(ii) λ = 1

(iii) All real values of λ except $\pm$ 1.