Hello I'm 14 years old so i don't know what a 4th degree polynomial is... however i agree with the guy named Kyouran. This is how i did it:
sqrt(x) + y = 11 ...(1)
sqrt(y) + x = 7 ...(2)
Let sqrt(x) = a, and sqrt(y) = b.
The eqs will then be:
a + b^2 = 11 ...(3)
b + a^2 = 7 ...(4)...