A system Ax = b with n unknowns has one solution if the rank of A is n.

A system $Ax = b$ with $n$ unknowns has one solution if the rank of $A$ is $n$. It has none if the rank of $A$ is smaller than the rank of the augmented matrix (the matrix $A$ with the column $b$ added). It has many solutions if the two ranks are equal and smaller than $n$. The function np.linalg.matrix_rank gives the rank. Classify these three systems.

1. $x + y = 3$ and $2x + 2y = 6$.
2. $x + y = 3$ and $2x + 2y = 7$.
3. $x + y = 3$ and $x - y = 1$.