If a linear system has no free variables, then it is consistent: Why is the statement false?

Question

I recently got this question wrong on a test, and I have no clue why. How can a system be inconsistent if there are no free variables?

Answer 1

Consider the "system" $x_1=2, x_1=3$. Are there any free variables?

Answer 2

Two equations (in 2 variables) that happen to be parallel lines form an inconsistent system. There are no free variables. Free variables means that there are infinite solutions. That is not incosistent.