We write x - y = 1 + s, s0 instead of x - y1.

The linear program then consists of a set of m (here m = 2) equations in n + m (here 4) variables, (x, y, z and s):

x + y + z = 2, x - y -s = 1, x0, y0, z0, s0, maximize x + 2z.