Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 62 / 3 / b / Solution

Use the standard form $Cz\le d$ with unrestricted $z=(x,y{)}^T$:The nonnegative multipliersatisfies $C^{T}w=0$ and $d^{T}w=-1<0$. 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 produceswhich directly exhibits the contradiction.