For the system of equations below check whether the two cond

For the system of equations below, check whether the two conditions in the Implicit Function Theorem are satisfied at point P = (1,1,1,1), where v and z are variables and x and y are parameters. If yes, find dz/dx, dz/dy, dv/dx, dv/dy at point P

x(z^3)+(y^2)(v^4)=2

xz + yvz^2=2

Solution

x(z³)+(y²)(v⁴)=1(1³)+(1²)(1⁴)

=1(1)+(1)(1)

=1+1

=2

xz+yvz²=(1)(1)+(1)(1)(1²)

  =1+1(1)

  =1+1

  =2

Yes, the two conditions in the Implicit Function Theorem are satisfied at the point P = (1,1,1,1).