Step-by-Step Solution
Key Concept: Homogeneous linear system with $D = \sqrt{2}(-\sqrt{8}) - \sqrt{3}(\sqrt{3}) = -4 - 3 = -7 <br>eq 0 \Rightarrow$ trivial solution $x = 0, y = 0$.
From 1st: $y = -\dfrac{\sqrt{2}}{\sqrt{3}}x$. Substitute in 2nd: $\sqrt{3}x - \sqrt{8}\left(-\dfrac{\sqrt{2}}{\sqrt{3}}x\right) = 0$. [1.0 Mark]
$\sqrt{3}x + \dfrac{4}{\sqrt{3}}x = 0 \Rightarrow \dfrac{7}{\sqrt{3}}x = 0 \Rightarrow x = 0 \Rightarrow y = 0$. Solution: $x = 0, y = 0$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Substitution: 1.0 Mark
Solving $x = 0, y = 0$: 1.0 Mark
Correct Answer: