Determine the solution of the simultaneous nonlinear equations as: $f_1(x_1{x}_2)=0$ and $f_2(x_1{x}_2)=0$

$(x_1-4{)}^2+(x_2-4{)}^2=4$

$x_1^2+x_2^2=16$

Use a graphical approach to obtain your initial guesses. Determine refined estimates with the two equation Newton$-$Raphson method by hand calculation.