1. \( x+y \geq 2 \)

Did you know that this inequality represents a region in a two-dimensional space? Specifically, it describes the area above and including the line \(x + y = 2\). Not only does this line have a positive slope, but any point (x, y) that satisfies this inequality must also lie in the first quadrant if both x and y are non-negative. This makes it a fundamental concept in linear programming, where we often need to maximize or minimize certain functions over defined regions! When solving inequalities like this, a common mistake is to overlook the need to express the solution set properly. It's essential to remember that when you graph inequalities, you must shade the entire solution region. Moreover, if there are multiple inequalities, be sure to find the intersection of their regions, as that will give you the feasible zone for solutions!