how to obtain transformation matrix A in y = Ax + b notation? I'm trying to obtain original transform matrix A and its translation vector b
From y=Ax+b equation. I have original values of vectors before transform and translation (x) and vectors after transform and translation (y)
I know that finding two unknowns with 1 equation is not possible, but I think if I arrange y=Ax+b in such a way that I can obtain A+b or A only? Is there is a way to find out?
And if I drop b from equation and try to find out matrix A only y = Ax when vectors y and x (2x1) are known and matrix A (2x2) is unknown, how I can do that? Because I can't take inverse of x 

We have 
$$\begin{align*}
\underset{2 \times 1}{y} = \underset{2 \times 2}{A}\times\underset{2 \times 1}{x} 
\end{align*}$$
Let $\underset{1 \times 2}{x^+}$ be the Moore-Penrose inverse of $x$ defined by
$$x^+ =\dfrac{x^\mathrm{T}}{\langle x,x\rangle}=\dfrac{x^\mathrm{T}}{x  x^\mathrm{T}}$$
Then we get that
$$
\begin{align*}
A = yx^+
\end{align*}$$
