Three equations with two unknowns can also be inconsistent.
For instance:
x = 4
y = 7
x + y = 1

(+ being the regular addition over Z, not addition modulo 10)

In that case, there is no solution.
Two equations with two unknowns can also be unsolvable. For instance:
x = y
x = y + 1
(Again, + being regular addition over Z)