For any initial guess of $x_0=[3,-1\mathrm{.}5],$ and a tolerance $t_{ol}=1e^{-14}.$

$x+e^{-x}+y^3=0$

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

i$.$ While using the Newton$-$Raphson procedure, find the solution within $(3$ steps$),$ including the initial step. Show your numerical hand steps details. $(5$ marks$)$

ii$.$ Write a MATLAB code to show how to solve the same problem numerically. $(5$ marks$)$