Which of the following describes the solution region for the system of inequalities: x ≥ 0, y ≥ 0, x + y ≤ 4?

Model Answer & Options

Source: Extra Practice

A triangular region in the first quadrant

An unbounded region in the first quadrant

A rectangular region in the first quadrant

A triangular region in the third quadrant

Explanation

The inequalities x ≥ 0 and y ≥ 0 restrict the solution to the first quadrant. The inequality x + y ≤ 4 represents the region below and on the line passing through (4,0) and (0,4). The intersection of these three constraints forms a closed triangular region with vertices (0,0), (4,0), and (0,4). It is bounded, making Option 2 wrong. It's not a rectangle (Option 3) and not in the third quadrant (Option 4).

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