Solve the following pair of linear equations | vedclass

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(A) Given equations are:$\sqrt{2} x + \sqrt{3} y = 0$ $...(1)$$\sqrt{3} x - \sqrt{8} y = 0$ $...(2)$From equation $(1)$,we express $x$ in terms of $y$

Vedclass · Accepted Answer

$x = 0, y = 0$

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(A) Given equations are:$\sqrt{2} x + \sqrt{3} y = 0$ $...(1)$$\sqrt{3} x - \sqrt{8} y = 0$ $...(2)$From equation $(1)$,we express $x$ in terms of $y$:$x = -\frac{\sqrt{3} y}{\sqrt{2}}$ $...(3)$Substituting the value of $x$ from equation $(3)$ into equation $(2)$:$\sqrt{3} \left( -\frac{\sqrt{3} y}{\sqrt{2}} \right) - \sqrt{8} y = 0$$-\frac{3 y}{\sqrt{2}} - 2\sqrt{2} y = 0$Factoring out $y$:$y \left( -\frac{3}{\sqrt{2}} - 2\sqrt{2} \right) = 0$Since the term in the bracket is non-zero,we must have $y = 0$.Substituting $y = 0$ into equation $(3)$:$x = -\frac{\sqrt{3} (0)}{\sqrt{2}} = 0$Thus,the solution is $x = 0$ and $y = 0$.

Solve the following pair of linear equations by the substitution method:
$\sqrt{2} x + \sqrt{3} y = 0$
$\sqrt{3} x - \sqrt{8} y = 0$

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Solve the following pair of linear equations by the substitution method:$\sqrt{2} x + \sqrt{3} y = 0$$\sqrt{3} x - \sqrt{8} y = 0$