Question

For which value(s) of λ do the pair of linear equations λx + y = λ² and x + λy = 1 have infinitely many solutions ?

• A. 0 and 1
• B. 0
• C. 1
• D. 0 and -1

Answer 1

The correct option is C 1

For infinitely many solutions,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\Rightarrow \frac{\lambda }{1}=\frac{1}{\lambda }=\frac{{\lambda }^2}{1}$

⇒ λ²=1

⇒λ=±1

Also, $\frac{\lambda }{1}=\frac{{\lambda }^2}{1}$

⇒ λ²=λ

⇒ λ² – λ=0

⇒ λ(λ–1)=0

⇒ λ=0, λ=1

∴ Common solution for which the pair of linear equations has infinitely many solutions is λ = 1 only.