= Solution
Use the standard form $Cz\leq d$ with unrestricted $z=(x,y)^T$:
$$
C=\begin{pmatrix}-1&0\\1&-1\\1&1\end{pmatrix},
\qquad d=\begin{pmatrix}0\\1\\-2\end{pmatrix}.
$$
The nonnegative multiplier
$$
\boxed{w=\begin{pmatrix}2\\1\\1\end{pmatrix}}
$$
satisfies $C^Tw=0$ and $d^Tw=-1<0$. This is a <Farkas certificate for linear inequalities>, so the system is infeasible by <Farkas lemma>. In scalar form, adding twice the first inequality to the other two produces
$$
\boxed{0\leq-1,}
$$
which directly exhibits the contradiction.
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