We do we consider VCE in the equations?
Like, this example didn't consider VCE in the equation at all. Why is that?

Equations 3b is wrong, \$V_{CE}\$ should be included.
Equation 3b should have been:
\$V_{CC}=I_C*R_C + V_{CE} + I_E * R_E\$
Equation 3a is correct and includes \$V_{BE}\$ like it should.