= System of linear inequalities
{title2=$Ax\leq b$}
A system of linear inequalities requires several <linear inequalities> to hold simultaneously. The notation $Ax\leq b$ compares coordinates componentwise, giving one <inequality> per row of the <matrix> $A$. Its <solution set> is the <intersection> of the corresponding <half-spaces>. For non-strict inequalities it is a <linear polyhedron>, which may be empty. For example, $x\geq1$, $y\geq1$, $x+y\leq1$ are inconsistent: adding their equivalent forms $-x\leq-1$, $-y\leq-1$, $x+y\leq1$ gives $0\leq-1$. A <Farkas certificate for linear inequalities> generalizes this cancellation.
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