What is the position of origin \((0,0)\) for \(x+y\geq 0\)?

Correct answer: on boundary and in solution

Substituting the origin \((0,0)\) gives \(x+y=0+0=0\). Hence, it lies on the boundary line \(x+y=0\). Since the inequality uses \(\geq\), the boundary line where equality holds is included in the solution region. Therefore, the origin is on the boundary and is also part of the solution. Exam tip: For \(\geq\) or \(\leq\), the boundary line is included.