Question

Question 1 (iii)
For which value (s) $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have a unique solution?

Answer 1

The given pair of linear equations is
$\lambda x+y=\lambda 2andx+\lambda y=1$
For a unique solution,
$\frac{a_1}{a_2}\ne \frac{b1}{b2}\Rightarrow \frac{\lambda }{1}\ne \frac{1}{\lambda }\Rightarrow {\lambda }^2\ne 1\Rightarrow \lambda \ne \pm 1$
So, all real values of $\lambda$ except $\pm$ 1