If \(x+2y\le10\), \(x\ge2\), \(y\ge1\), which two vertices lie on \(x+2y=10\)?

Correct answer: \((2,4)\) and \((8,1)\)

On the boundary line \(x+2y=10\), put \(x=2\). Then \(2+2y=10\), so \(y=4\) and one vertex is \((2,4)\). Similarly, putting \(y=1\) gives \(x+2=10\), so \(x=8\) and the other vertex is \((8,1)\). The points in option D lie on the line, but they are not vertices formed by intersections with the boundary lines \(x=2\) and \(y=1\). Exam tip: find vertices by checking intersections of pairs of boundary lines.