Question: Solve the following equations by the Newton-Raphson method: [ begin{array}{r} 2 x_{1}+x_{2}^{2}-8=0 x_{1}^{2}-x_{2}^{2}+x_{1} x_{2}-3=0 end{array} ] Start with an initial guess of (x_{1}=1) and

Solve the following equations by the Newton-Raphson method:
\[
\begin{array}{r}
2 x_{1}+x_{2}^{2}-8=0 \\
x_{1}^{2}-x_{2}^{2}+x_{1} x_{2}-3=0
\end{array}
\]
Start with an initial guess of $x_{1}=1$ and $x_{2}=1$.

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