Question
Which value(s) of $\lambda,$ do the pair of linear equations $\lambda\text{x}+\text{y}=\lambda^2$ and $\text{x}+\lambda\text{y}=1$have:
a unique solutions?
a unique solutions?
✓
Answer
For a Unique solution,$\frac{\text{a}_1}{\text{a}_2}\neq\frac{\text{b}_1}{\text{b}_2}$
$\Rightarrow\frac{\lambda}{1}\neq\frac{1}{\lambda}$
$\Rightarrow\lambda^2\neq1$
$\Rightarrow\lambda\neq\pm1$
So, all real values of $\lambda$ except $\pm1$
$\Rightarrow\frac{\lambda}{1}\neq\frac{1}{\lambda}$
$\Rightarrow\lambda^2\neq1$
$\Rightarrow\lambda\neq\pm1$
So, all real values of $\lambda$ except $\pm1$
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