Question

Is the answer written aside the question correct. answer whether wrong.........,

Answer 1

It is right.
Answer is last option i.e,
x = 0 & y = 0.

Answer 2

it's wrong you can't multiply a non root value to the square root
3*√2=3√2
not √6
if you want to solve the question u have to multiply it like it is given below
(√2)x+(√3)y=0 * √3
(√6)x+(√9)y=0
(√6)x+3y=0
for second equation
(√3)x-(√8)y= 0 * √2
(√6)x-(√16)y=0
(√6)x-4y= 0
now you may proceed as the same
answer will be same