Where is the point ((2,3)) located with respect to (x+y\leq 5), (x\geq 1), and (y\leq 4)?

Correct answer: In the solution region and on the boundary (x+y=5)

A point satisfies the system only when all three conditions are true. For (2,3), the first condition gives \(x+y=2+3=5\), so \(x+y\leq5\) is true and the point lies exactly on the boundary \(x+y=5\). The second condition is \(x=2\geq1\), which is true. The third is \(y=3\leq4\), also true.

Thus (2,3) is inside the solution set, but it is on one of its boundary lines. It is not on the boundaries \(x=1\) or \(y=4\), because its coordinates are 2 and 3. Therefore the precise description is “in the solution region and on the boundary \(x+y=5\),” which is choice A. The equality is allowed because the first inequality uses \(\leq\).