1. Since the determinant of the coefficient matrix is equal to zero, there is either no solution or an infinite number of solutions. I haven't checked your work but assuming that x - 3z = 4 and y - 2z = 5 are correct, the solution can be written as

x = 3t + 4, y = 2t + 5, z = t

where t is any real number. That is, an infinite number of solutions.

2. Assuming that a polynomial of minimum degree is required, you should use the model and substitute the given data to get three equations involving a, b and c. Solve these equations simultaneously.