Which region is represented together by (x\geq 1) and (y\geq 2)?

Correct answer: right of (x=1) and above (y=2)

The direct answer is option B: the region to the right of \(x=1\) and above \(y=2\), including both boundary lines. The inequality \(x\geq1\) means that a point's x-coordinate is 1 or greater, so the point lies on or to the right of the vertical line \(x=1\). The inequality \(y\geq2\) means that its y-coordinate is 2 or greater, so the point lies on or above the horizontal line \(y=2\). To satisfy both inequalities together, take the common overlapping region: right and above. Since both signs include equality, the lines \(x=1\) and \(y=2\) are included and should be solid boundaries. Option A says left and below, which would represent \(x\leq1\) and \(y\leq2\), the opposite directions. Option B is correct because every point there has both required coordinates. Option C, only \((1,2)\), is too small; many points such as \((2,3)\), \((5,2)\), and \((1,6)\) satisfy both inequalities. Option D, the whole plane, includes points such as \((0,0)\), which fail both conditions. A quick test point in the correct region is \((2,3)\): \(2\geq1\) and \(3\geq2\). Memory cue: x inequalities move left-right, y inequalities move up-down; combine them by taking the overlap.