Background
- Solve the following set of nonlinear equations by the Gauss-Seidel method:
$$\left\{\begin{array}{ll} 27x+e^x \cos\ y -0.12z & =\ 3, \\ -0.2x^2+37y+3xz &=\ 6, \\ x^2-0.2y \sin x+29z & =-4. \end{array}\right.$$
$\quad $ Start with an initial guess of $x=y=z=1.$
I'm trying to implement Gauss-Seidel method in $C$ with the following set of equations. I can't for the life of me figure out how to solve for $x$. It is pretty straight forward to solve for y and solve for $x$. I would really be appreciative is someone knows a way to isolate $x$ so I can start iterating through. Thanks so much for any thoughts.
My Understanding
This is what I have thus far:
From eqn 2)$$ y = \frac{(6-3xz+.2x^2)}{37} $$
From eqn 3)$$ z = \frac{-4+.2y\sin{x}-x^2}{29}$$
This is where I am stuck
$$ 27x + e^{x}\cos{y} = 3+.12z$$