Question

root 2 x minus root 3 Y is equal to zero and root 5 x + root 2 Y is equal to zero



solve the following question by elimination method​

Answer 1

Answer:

.......

x=0 y=0...... .

Answer 2

Answer:

The solution of the given equation is $(0,0)$.

Step-by-step explanation:

Consider the equations as follows:

$\sqrt{2} x-\sqrt{3}y=0$ ...... (1)

$\sqrt{5} x+\sqrt{2}y=0$ ...... (2)

Using elimination method,

Multiply the equation (1) by $\sqrt{2}$ as follows:

⇒ $\sqrt{2} (\sqrt{2} x-\sqrt{3}y)=\sqrt{2} (0)$

Simplify as follows:

⇒ $\sqrt{2} \sqrt{2} x-\sqrt{2} \sqrt{3}y=0$

⇒ $2 x-\sqrt6}y=0$ (Since $\sqrt{2} \sqrt{2}=2$ and $\sqrt{2} \sqrt{3}=\sqrt{6}$) ...... (3)

Now,

Multiply the equation (2) by $\sqrt{3}$ as follows:

⇒ $\sqrt{3} (\sqrt{5} x+\sqrt{2}y)=\sqrt{3} (0)$

Simplify as follows:

⇒ $\sqrt{3} \sqrt{5} x+\sqrt{3} \sqrt{2}y=0$

⇒ $\sqrt15}x+\sqrt{6}y =0$ (Since $\sqrt{3} \sqrt{5}=\sqrt{15}$ and $\sqrt{3} \sqrt{2}=\sqrt{6}$) ...... (4)

Add equation (3) and (4) as follows:

$\sqrt15}x+\sqrt{6}y +(2x-\sqrt{6}y )=0$

⇒ $\sqrt15}x+\sqrt{6}y +2x-\sqrt{6}y =0$

Further, simplify as follows:

⇒ $\sqrt15}x -2x =0$

⇒ $(\sqrt15} -2)x =0$

⇒ $x=0$

Substitute the value of $x$ in equation (4), we get

$\sqrt15}(0)+\sqrt{6}y =0$

⇒ $0+\sqrt{6}y =0$

⇒ $\sqrt{6}y =0$

⇒ $y =0$

The value of $x=0$ and $y=0$.

Therefore, the solution of the given equation using elimination method is $(0,0)$.

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