Find the value of ' $l$ ' for which the system of equations
$3 x + y = 1$ ,
$(2 l - 1) x + (l - 1) y = (2 l + 1)$ has no solution.

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Solution

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
$\Rightarrow \frac{3}{2 ℓ - 1} = \frac{1}{ℓ - 1} \neq \frac{1}{2 ℓ + 1}$
$\Rightarrow 3 l - 3 = 2 ℓ - 1$
$\Rightarrow ℓ = 2$
$2 ℓ + 1 \neq ℓ - 1$
$\Rightarrow ℓ \neq - 2$

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