Solve linear equation with 2 unkown and 3 equations in numpy with np.linalg.solve

Question

3 euqations with two unknow have 3 solutions: One solution, infinte solutions, no solution. How would you write this in Numpy to get the solutions? I tried it the way you would do it with 3 unknowns:

import numpy as np

a = np.array([-9,-8, 14])

A = np.array([[ 1, 2, -2],
              [-3,-1, 4],
              ])
x = np.linalg.solve(A, a)
print(x)

But gives an Error, as A is not square. Sadly if I remove the last column of a and A, although i get an answer the system might still have no solution as it might not fit in the third equation.