The three non-linear equations are given by

\begin{equation}

c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0

\end{equation}

\begin{equation}

s[2.001 *c + 835(1-q)]-2.001*c =0

\end{equation}

\begin{equation}

q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c =0

\end{equation}

Using the Newton-Raphson Method solve these equations in terms of $c$,$s$ and $q$.

=> It is really difficult question for me because i don't know very much about the Newton-Raphson Method and also these non-linear equations contain 3 variables.

I have try by applying the newton-Raphson method to each equations:-

\begin{equation}

f(c,s,q)=0= c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532

\end{equation}

\begin{equation}

g(c,s,q)=0= s[2.001 *c + 835(1-q)]-2.001*c

\end{equation}

\begin{equation}

h(c,s,q)=0= q[2.73 + (5.98*10^{10})c]-(5.98 *10^{10})c

\end{equation}

now i guess i need to work out $f'(c,s,q), g'(c,s,q), h'(c,s,q)$ but i dont know how?

and after working out $f'(c,s,q), g'(c,s,q), h'(c,s,q)$ . After that i think i need to use newton-raphson iteration:

$c_{n+1}= c_n - \frac{f(c,s,q)}{f'(c,s,q)}$

but the $f(c,s,q)$ and $f'(c,s,q)$ contains the $s$ and $q$.

Similarly, for

$s_{n+1}= s_n - \frac{g(c,s,q)}{g'(c,s,q)}$

will have $g(c,s,q)$ and $g'(c,s,q)$ containing the $c$ and $q$.

$q_{n+1}= q_n - \frac{h(c,s,q)}{h'(c,s,q)}$

will have $h(c,s,q)$ and $h'(c,s,q)$ containing the $c$.

so am i not sure what to do please help me. to find the values of $c,s,q$.