Question

Solve the following pair of linear equations by elimination method

$\sqrt{7}x+\sqrt{11}y=0$ and $\sqrt{3}x-\sqrt{5}y=0$

• A. $x=0,y=0$
• B. $x=1,y=1$
• C. $x=7\sqrt{11},y=5\sqrt{3}$
• D. Data insufficient

Answer 1

Answer: (A)

$x=0,y=0$

$\sqrt{7}x+\sqrt{11}y=0$ ......(i)
$\sqrt{3}x-\sqrt{5}y=0$ ......(ii)
On multiplying equation (i) by $\sqrt{3}$ and equation (ii) by $\sqrt{7}$. we get,
$\sqrt{21}x+\sqrt{33}y=0$ ......(iii)
$\sqrt{21}x-\sqrt{35}y=0$ ......(iv)
On subtracting equation (iv) from equation (iii). we get,
$\sqrt{21}x+\sqrt{33}y=0$
$\underset{–}{\underset{-}{\sqrt{21}}x-\underset{+}{\sqrt{35}}y=\underset{-}{0}}$
$(\sqrt{33}+\sqrt{35})y=0$
$\Rightarrow y=0$
On substituting $y=0$ in equation (i). we get,
$\sqrt{7}x+\sqrt{11}\times 0=0$
$\Rightarrow \sqrt{7}x=0$
$\Rightarrow x=0$
$\therefore x=0,y=0$
Option A is correct.