Answer
See sample answer below
Work Step by Step
An inconsistent system has no solutions.
Its equations represent parallel lines.
So, take line 1 to be $y=x$ and line 2 to parallel to it, $y=x+2$
The two lines have no intersections, so the system $\left\{\begin{array}{l}
y=x\\
y=x+2
\end{array}\right.$
has no solutions and is inconsistent.
