Given that `x tan 30^(@)+y cot 60^(@)=0`

`or, x xx (1)/(sqrt(3)) +y xx (1)/(sqrt(3))=0 or, x+y=0 ["multiplying by " sqrt(3)] ……………..(1)`

Again, `2x-y tan45^(@) =1 " " or, 2x-y xx 1=1 " " or, 2x-y=1 ……..(2)`

Adding (1) and (2) we get, `3x=1 " " or, x=(1)/(3).`

`therefore `from (1) we get, `(1)/(3)+y=0 " " or, y=-(1)/(3).`

Hence the values of `x=(1)/(3) and y=-(1)/(3)`.