Question: Newton's Method and Nonlinear Systems

Does anyone know a command for using Newton's method to a solve a nonlinear system, particularly this one:

4y^2+4y+52x=19

169x^2+3y^2+111x-10y=10

?

 

Also, how about this one:

x+e^-1x+y^3=0

x^2+2xy-y^2+tan(x)=0

 

?

 

Thank you

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