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Solve for $x$ and $y$: $\sqrt{2}x + \sqrt{3}y = 5$ and $\sqrt{3}x - \sqrt{8}y = -\sqrt{6}$
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$(\sqrt{2}x + \sqrt{3}y = 5) \times \sqrt{3} \implies \sqrt{6}x + 3y = 5\sqrt{3}$
$(\sqrt{3}x - \sqrt{8}y = -\sqrt{6}) \times \sqrt{2} \implies \sqrt{6}x - 4y = -2\sqrt{3}$
Solving the equations, we get $x = \sqrt{2}$ and $y = \sqrt{3}$
$(\sqrt{3}x - \sqrt{8}y = -\sqrt{6}) \times \sqrt{2} \implies \sqrt{6}x - 4y = -2\sqrt{3}$
Solving the equations, we get $x = \sqrt{2}$ and $y = \sqrt{3}$