The common region for all the inequalities y ≥ 2, y ≤ 2x + 2and x + y ≤ 4 is represented by ΔABC (the last graph)
What is an inequality?
"It is a statement which consists of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two mathematical expressions."
For given question,
We have been given three inequalities
y ≥ 2 ,
x + y ≤ 4 ,
y ≤ 2x + 2
If we draw the graph of these three inequalities then the common region represents the all the points that fulfill all three inequalities.
An inequality y ≥ 2 represents all the points on and above the line y = 2
An inequality x + y ≤ 4 represents all the points on and below the line x + y = 4
An inequality y ≤ 2x + 2 represents all the points on and below the line y = 2x + 2
Consider the following graphs.
The first graph represents the points which fulfill the inequality y ≥ 2
The graph for an inequality x + y ≤ 4 is represented by the shaded blue region.
The graph for an inequality y ≤ 2x + 2 is represented by the shaded green region.
The common region for all the inequalities is represented by ΔABC
Learn more about inequality here:
https://brainly.com/question/19003099
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