The set of equations 2x+3y+4z=0, 3x+4y+6z=0, 4x+5y+8z=0

Infinite solutions

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is inconsistent

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has unique solution

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has two solutions

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Solution

The correct option is A Infinite solutions
Given, $2 x + 3 y + 4 z = 0, 3 x + 4 y + 6 z = 0, 4 x + 5 y + 8 z - 0$
$∴ Δ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & 3 & 4 3 & 4 & 6 4 & 5 & 8 \end{matrix} ∣ ∣ ∣ ∣$
$= 4 - 4 = 0$
$∴ Δ = 0$ so infinite solutions.

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