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Question
Find the linear inequalities for which the shaded region in the given figure is the solution set.
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Solution
Considering x + y = 8, the shaded region and the origin both are on the same side of the graph of the line and (0, 0) satisfy the constraint x + y ≤ 8.
Considering x + y = 4, the origin is on the opposite side of the shaded region and (0, 0), Hence, doesn’t satisfy the constraint x + y ≥ 4. Therefore required constraint is x + y ≥ 4.
We see that, The shaded region is in the first quadrant i.e. x ≥ 0 and y ≥ 0, Also, shades region is below the line y = 5 and left to the line x = 5.
⇒ y ≤ 5 and x ≥ 5
Hence, the linear inequalities are x + y ≤ 8, x + y ≥ 4, x ≥ 0, y ≥ 0, x ≤ 5, y ≤ 5.
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