Real analysis problem that I need some help with. The question is attached as a picture. Thanks!

10. Consider the two equations Fi(x, y, u, v) =er"-y'us - 13 = 0 F2(x, y, u, u) =e" -vx? - y? = 0 Prove that there exists a neighborhood, U, of (1, 1) E R? and functions u(x, y) and v(x, y) on U with u(1, I ) = v(1, 1) = 1 such that - Fi (x, y, u(x, y), v(x, y)) = F2 (x, y, u(x, y), v(x, y)) = 0 Vx, y E U. Find Ou(r, y) (1,1)