The value of - for which the lines 3 x -4 y -5-5 x -4 y -4 and - x -4 y -6 meet at a point isA- 2B- 4C- 3D- 1

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Condition for Concurrency of Three Lines

The value of ...

Question

The value of $λ$ for which the lines $3 x + 4 y = 5, 5 x + 4 y = 4$ and $λ x + 4 y = 6$ meet at a point is

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Solution

The correct option is B
1

It is given that the lines $3 x + 4 y = 5, 5 x + 4 y = 4$ and $λ x + 4 y = 6$ meet at a point.

In other words, the given lines are concurrent.

$∣ ∣ ∣ ∣ \begin{matrix} 3 & 4 & - 5 5 & 4 & - 4 λ & 4 & - 6 \end{matrix} ∣ ∣ ∣ ∣ = 0$

$\Rightarrow 3 (- 24 + 16) - 4 (- 30 + 4 λ) - 5 (20 - 4 λ) = 0$

$\Rightarrow - 24 + 120 - 16 λ - 100 + 20 λ = 0$

$\Rightarrow 4 λ = 4$

$\Rightarrow λ = 1$

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The value of λ for which the lines 3x+4y=5, 5x+4y=4 and λx+4y=6 meet at a point is

The correct option is B 1 It is given that the lines 3x+4y=5, 5x+4y=4 and λx+4y=6 meet at a point. In other words, the given lines are concurrent. ∣∣ ∣∣34−554−4λ4−6∣∣ ∣∣=0 ⇒ 3(−24+16)−4(−30+4λ)−5(20−4λ)=0 ⇒ −24+120−16λ−100+20λ=0 ⇒ 4λ=4 ⇒ λ=1

The value of $λ$ for which the lines $3 x + 4 y = 5, 5 x + 4 y = 4$ and $λ x + 4 y = 6$ meet at a point is