Simultaneous equations using Gaussian Elimination Method - Math AAHL IBDP
This longer video explains how to use GEM, to get the solutions to a set of 3D planes (xyz). The way I've explained it is an inefficient method, because I go into depth with every step, however, may you wish to, you can concatenate your operations (one such concatenation could be R_2=3R_1-2R_2 and R_3=R_1-2R_3 in one step instead of forming two matrices).