Solve the following system of equations:

$\sqrt{2}x\ –\ \sqrt{3}y\ =\ 0$
$\sqrt{3}x\ −\ \sqrt{8}y\ =\ 0$


Given: The pair of linear equation are  $\sqrt{2}x\ –\ \sqrt{3}y\ =\ 0$ ;

$\sqrt{3}x\ −\ \sqrt{8}y\ =\ 0$


To do: Solve the system of equations


Solution:

The given pair of equations are:

 $\sqrt{2}x\ –\ \sqrt{3}y\ =\ 0$=
0…………i)

 

$\sqrt{3}x\ −\ \sqrt{8}y\ =\ 0$…………ii) 


From equation i) $ x = \sqrt(\frac{3}{2})y$ ……………..iii)


Substituting this value in equation ii) we obtain


$\sqrt{3}x\ −\ \sqrt{8}y\ =\ 0$


$\Rightarrow \sqrt{3}\left(\sqrt{\frac{3}{2}}\right) -\sqrt{8} y=0$


$\Rightarrow \frac{3}{\sqrt{2}} -8y=0$


$\Rightarrow 3y-4y = 0$


$\Rightarrow y=0$


Now, substituting y in equation iii) we obtain 


$\Rightarrow x = 0$ 


Thus, the value of $x$ and $y$ obtained are $0$ and $0 $respectively  

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Updated on: 10-Oct-2022

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