A system of linear equations, or a linear system, is a collection of one or more linear equations involving the same variables. An example is
2x₁ - x₂ = 0
x₁ + x₂ = 3
The solution of the system of the above two equations in two variables is easy- it amounts to finding the intersection of two lines.

The essential information of a linear system can be recorded compactly in a rectangle array called a matrix. Given the above system wiht the coefficients of each variable aligned in columns, the matrix sympy.Matrix([[2, -1], [1, 1]]) is called the coefficient matrix or matrix of coefficients of the system. And the matrix sympy.Matrix([[2, -1, 0], [1, 1, 3]]) is called the augmented matrix of the system. An augmented matrix of a system consists of the coefficient matrix with an added column containing the constants from the respective right sides of the equations.