Question

Solve $3\sqrt{2}x-5\sqrt{3}y+\sqrt{5}=0$
$2\sqrt{3}x+7\sqrt{2}y-2\sqrt{5}=0$

Answer 1

$3\sqrt{2}x-5\sqrt{3}y+\sqrt{5}=\mathrm{0.........}\left(i\right)$
$2\sqrt{3}x+7\sqrt{2}y-2\sqrt{5}=\mathrm{0.........}\left(ii\right)$
Multiplying (i) by $2\sqrt{3}$ and (ii) by $3\sqrt{2}$
$6\sqrt{6}x-10\times 3y=-2\sqrt{15}$
$6\sqrt{6}x+21\times 2y=6\sqrt{10}$
- - -
Subtracting $-72y=-(6\sqrt{10}+2\sqrt{15})$
or $72y=6\sqrt{10}+2\sqrt{15}\Rightarrow y=\frac{6\sqrt{10}+2\sqrt{15}}{72}$
$\therefore x=\frac{10\sqrt{15}-7\sqrt{10}}{72}$