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Question

For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?

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Solution

The given pair of linear equations is
λx+y=λ2 and x+λy=1
For a unique solution,
a1a2b1b2

Here, a1=λ,b1=1 and a2=1,b2=λ

λ11λ

λ21λ±1

So, for all real values of λ except ± 1, the given pair of linear equations will have a unique solution.


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