Setting y = 0 and z = 0 leads to s = 1, x = 1, which point obeys all the constraints.
We may therefore choose y and z as basis variables and solve for x and s.
We get

x = 2 - y - z, s = 1 -2y -z

We also write the objective function in terms of the basis variables:

OF = x + 2z = 2 - y + z

The value of the objective function at the origin in this basis is 2.
If we take z out of the basis, and put s in instead, the objective function at the origin increases;
We get

z = 1 - 2y - s, x = 2 - y - z = 1 + y + s

and the objective function is

3-3y-s

Obviously this cannot exceed 3 if y and s are to be positive, so that 3 is the solution for the objective function, and the solution point is z = 1, x = 1, y = s = 0.