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Question: Which of the graphs defines the system of inequalities, x + y < 3, -5x + 2y ≤ 10, y ≥ -3?



A ) Graph-1
B ) Graph-2
C ) Graph-3
D ) Graph-4

Steps to derive

1 Graph all the three inequalitites in the same coordinate plane.


2 The graph of x + y < 3 is the half-plane below the dashed line x + y = 3.

3 The graph of -5x + 2y ≤ 10 is the half-plane on and below the solid line -5x + 2y = 10.

4 The graph of y ≥ -3 is the half-plane on and above the solid line y = -3.

5 The graph of the system is the intersection of the three half planes as shown in the graph.

6 Graph-1 is the correct answer.



Hence the right answer is Option A

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