The equation which cannot be solved in integers is
\(5y - 3 = -18\)
\(3x - 9 = 0\)
\(3z + 8 = 3 + z\)
\(9y + 8 = 4y - 7\)
\(3z + 8 = 3 + z \implies 2z = -5 \implies z = -\dfrac{5}{2}\), not an integer.