10. Lorenz derive a simple system of ordinary differential equations describing buoyant convection in a fluid as a crude model for atmospheric circulation. At steady state, the convective velocity, z, temperature gradient y, and heat flow z satisfy the system of nonlinear equations o(y-x) = 0, rx-y-xz = 0, ry-bz = 0, where (the Prandtl number), r (the Rayleigh number), and b are positive constants that depend on the properties of fluid, the applied temperature gradient, and the geometry of the problem. Typical values Lorenz used are o = 10, r = 28, and b = 8/3. Write a code using Newton's method to solve this system of equations.