This is a question from my Analysis textbook

3. Prove that there exist functions u(x,y), v(x,y) and w (x,y) and an r>0 such that u,v,w are continuously differentiable and satisfy the equations

u^5+xv^2-y+w=0

v^5+yu^2-x+w=0

w^4+y^5-x^4=1

on Br(1,1) and u(1,1)=1, v(1,1)=1, w(1,1)=-1