Linear system/Equating method/Remark

Another method to solve a linear system is the equating method. Here, the variables are also successively eliminated, but in another way. In this method, in every equation , , we isolate one fixed variable, say . Suppose that (after reordering) are the equations where the variable occurs with a coefficient different from . These equations are brought into the form

where in , the variable does not occur. The linear system consisting in

is equivalent to the original system. We continue with this system without .