Question

Question 1 (ii)
For which value (s) $\lambda$, do the pair of linear equations $\lambda x+y={\lambda }^{2}andx+\lambda y=1$ have infinitely many solution.

Answer 1

The given pair of linear equations is
$\lambda x+y=\lambda 2andx+\lambda y=1a_1=\lambda ,b_1=1c_1=-{\lambda }^2{a}_2=1,b_2=\lambda ,c_2=-1$
For infinitely many solutions,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\frac{\lambda }{1}=\frac{1}{\lambda }\ne \frac{{\lambda }_2}{1}\Rightarrow \frac{\lambda }{1}=\frac{{\lambda }_2}{1}\Rightarrow \lambda (\lambda -1)=0When\lambda \ne 0,then\lambda =1$