The following system of equations defines x = x(u, v)and Y =y(u, v) as differentiable functions of u and v around the point P(x, y, u, v) = (1,4, 1, −1).

y² + 2u² + v² -xy = 15

2y² + u² + v² +xy= 38.

Think of u and v as exogenous (i.e., independent) variables and x and y as endogenous (i.e., dependent) variables. Answer the following questions.

1. Find the differentials of x and y expressed in terms of the differentials of u and v.

2. Use Cramer's rule to find dx/du and dy/du at P.

3. Use Cramer's rule to find dx/dv and dy/dv at P.

4. Compute the approximate values of x and y that correspond to u =0.9 and v= -1.1.