If an inhomogeneous system of equations has more equations than variables, it has no solution.
Proof:
Let $I$ be an inhomogeneous system of equations:
\begin{align}
a_{11}x_1&=b_1\\
a_{12}x_1&=b_2 \quad \text{ with }a_{11},a_{12}=1
\end{align}
Case 1: $b_1=b_2$
Both equations are equivalent.
Case 2: $b_1 \neq b_2$
In order to solve this system of equations, the equation $x_1=b_1=b_2=x_1$ must hold. This is obviously not possible, because $b_1\neq b_2$. Therefore, the system of equations has no solution. $_\blacksquare$
Is this a proper proof? It's seems a bit too simple.
Best Answer
The system
$$x+y=2$$ $$2x+2y=4$$ $$3x+3y=6$$ has $(1/1)$ as a solution although we have three equations but only two variables. So, the claim is false.