## Question

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

## Detailed Solution

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

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