Find all solutions to the following nonlinear system of equations: Does your an...

Find all solutions to the following nonlinear system of equations:

Does your answer contradict Theorem 2.5.9? Explain.

Reference Theorem 2.5.9: Consider the m×n linear system Ax = b. Let r denote the rank of A, and let r^# denote the rank of the augmented matrix of the system. Then

1. If r < r^#, the system is inconsistent.

2. If r = r^#, the system is consistent and

(a) There exists a unique solution if and only if r^# = n.

(b) There exists an infinite number of solutions if and only if r^# < n.