I'm doing my homework but I'm lost on one thing. Lets say that we have a systems of equations like so: 2x1+3x2=y1 4x1+2x2=y2 Instead of setting it to a constant our teacher sets it to a variable, he says that to be able to compute this, the augmented matrix should look like: 2 3|1 0 4 1|0 1 Then of course we find the echelon form. Does this have a name? The fact that he sets it to another variable or the way the augmented matrix is set up? I'm trying to learn more about them but my professor almost never follows the regular curriculum. Thank you in advance.