Solve the following systems of equations: 2x-3y=0, 3x-8y=0. - Vidyadip

Question

Solve the following systems of equations:
$\sqrt{2}\text{x}-\sqrt{3}\text{y}=0,$
$\sqrt{3}\text{x}-\sqrt{8}\text{y}=0.$

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Answer

The given equations are,
$\sqrt{2}\text{x}-\sqrt{3}\text{y}=0\ ......(\text{i})$
$\sqrt{3}\text{x}-\sqrt{8}\text{y}=0\ .....(\text{ii})$
Multiplying (i) by $\sqrt{3}$ and (ii) by $\sqrt{2}$ we get,
$\Rightarrow\sqrt{6}\text{x}-3\text{y}=0\ ......(\text{iii})$
$\Rightarrow\sqrt{6}\text{x}-4\text{y}=0\ ......(\text{iv})$
Subtracting (iii) from (iv) we get,
$\Rightarrow-\text{y}=0$
$\Rightarrow\text{y}=0$
Putting y = 0 in (i) we get,
$\Rightarrow\sqrt{2}\text{x}-\sqrt{3}\times0=0$
$\Rightarrow\sqrt{2}\text{x}-0=0$
$\Rightarrow\sqrt{2}\text{x}=0$
$\Rightarrow\text{x}=0$
Thus, the solution is x = 0 and y = 0.

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