## Question

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The solution of linear inequalities x + y ≥ 5 and x – y ≤ 3 lies

## Answer (Detailed Solution Below)

## Detailed Solution

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Concept:

Draw the constraints to find the feasible region:

- To draw the inequalities, first, draw the equation form of the inequalities.
- Now check the region which we have to choose depending on the sign of inequality.
- To check which region we need to choose put (0,0) in both the inequality. and check whether this inequality is satisfying or not.
- If it is satisfying the inequality then take the region containing (0,0) else the opposite side of (0,0).

Calculation:

Given: x + y ≥ 5

⇒ y ≥ – x + 5

- The given linear inequality covers the area (shaded region) above the straight line y = – x + 5 as shown below,

Similarly, x – y ≤ 3

⇒ – y ≤ – x + 3

⇒ y ≥ x – 3

- The given linear inequality covers the area (shaded region) above the straight line y = x – 3 as shown below,

- Hence, the solution of the two linear inequalities is the common area (shaded region) covered by the two inequalities as shown below,

∴ The solution to the given linear inequalities lies in the first and second quadrants.

Last updated on Aug 10, 2023

UPSC CDS 2 Admit Card Out on 10th August 2023! Candidates will be able to download the CDS admit card till 3rd September 2023, i.e., the CDS 2 2023 exam date. UPSC CDS 2 2023 Notification was out earlier for a total of 349 vacancies. Interested candidates applied for the exam from 17th May to 6th June 2023. The candidates will have to undergo a selection process which will have a written test and then an Interview. The candidates must be between the age of 20 and 24 years to be eligible Refer to the CDS Previous Year Papers to enhance your preparation. Also, attempt the CDS Mock Test.