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The linear inequations, for which the shaded area in the figure given below is the solution set, are

The linear inequations, for which the shaded area in the figure given below is the solution set, are Correct Answer 2x + 6y ≤ 21, 5x – 2y ≤ 10

The given region is below the line 5x – 2y = 10 and below the line 2x + 6y = 21

2y ≥ 5x – 10

⇒ 10 ≤ 5x – 2y

6y ≥ 21 – 2x

⇒ 2x + 6y ≥ 21

⇒ The required region is 2x + 6y ≤ 21, 5x – 2y ≤ 10

This can be checked by taking the origin as the test point

2(0) + 6(0) = 0 ≤ 21

5(0) – 2(0) ≤ 10

∴ The required region is 2x + 6y ≤ 21, 5x – 2y ≤ 10

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