Final answer:
To solve the system of nonlinear equations using the Underrelaxed Gauss-Seidel Method, iterative substitution of the most recently calculated values is used until convergence. The initial guess is given as 5^(12.9) for both x and y. The unrelated equations and values given do not apply to this problem.
Step-by-step explanation:
The solution of the system of nonlinear equations x² = 5 - y and y + 1 = x² can be approached using numerical methods, such as the Underrelaxed Gauss-Seidel Method. Given the initial guess for both x and y as 5^(12.9), we start by solving the first equation for y in terms of x, and then the second equation for x in terms of y.
Assuming we apply the Gauss-Seidel iterative process, we would use the current or most recently updated values for the variables at each step. After the first variable is updated, its new value is used to calculate the next variable within the same iteration.
However, the information provided regarding 'substituting 2.0× for x' and specific values for y do not directly apply to the given question and may come from a different problem context. Likewise, the mention of equations involving 'yo', 'vot', 'at²', 'dx²-y²' and 'KErel' do not correlate with the presented system of equations. When conducting the Gauss-Seidel method, one would iteratively substitute and solve until the values converge to a stable solution with a pre-defined tolerance level.