Do the left and right "parts" of the matrix used when performing Gaussian Elimination have names?

Question

Given a matrix used to perform Gaussian Elimination like this:

$$ \begin{bmatrix} 1 & -3 & | & 1 \\ 2 & -7 & | & 3 \end{bmatrix} $$

Which would be derived from a system of equations like this:

$$ \begin{cases} x - 3y = 1 \\ 2x - 7y = 3 \end{cases} $$

Do the different "sides", i.e. the parts that come from the right hand side of the equation and the part that comes from the left hand side of the equation, respectively, have names?

Answer 1

The left side is the coefficient matrix, and the right side is the column vector of constant terms.

Together, they comprise an augmented matrix.