High School Math Challenge

we are given $y^{2}+xy=36.............(1)$ , and $x^{2}-y^{2}=9....................(2)$ ,adding these two we get $x^{2}+xy=45............................................(3)$ now adding (1)&(3) we get $(x+y)^{2}=81$ which gives $x+y=\boxed{9}$

hmm, it seems I should edit both the answer and question as this question should actually involve the factorization of both equations 1 and 4

X ^ { 3 } - y ^ { 3 } = 61

5 ^ { 3 } - 4 ^ { 3 } =61

X ^{ 2 } -Y ^ { 2 } = 9

5 ^ { 2 } - 4 ^ { 2 } = 9 and so on ....it worked with all these equations

it is given that (x+y)(x-y)=9 therefore (5+4)(5-4)=9 hence x+y=9