How can I solve system of linear equations in SymPy?

SymPy recently got a new Linear system solver: linsolve in sympy.solvers.solveset, you can use that as follows:

In [38]: from sympy import *

In [39]: from sympy.solvers.solveset import linsolve

In [40]: x, y, z = symbols('x, y, z')

List of Equations Form:

In [41]: linsolve([x + y + z - 1, x + y + 2*z - 3 ], (x, y, z))
Out[41]: {(-y - 1, y, 2)}

Augmented Matrix Form:

In [59]: linsolve(Matrix(([1, 1, 1, 1], [1, 1, 2, 3])), (x, y, z))
Out[59]: {(-y - 1, y, 2)}

A*x = b Form

In [59]: M = Matrix(((1, 1, 1, 1), (1, 1, 2, 3)))

In [60]: system = A, b = M[:, :-1], M[:, -1]

In [61]: linsolve(system, x, y, z)
Out[61]: {(-y - 1, y, 2)}

Note: Order of solution corresponds the order of given symbols.