Exercise Ex. 6.1

Solution 1

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Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

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Solution 14

Solution 15

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Solution 18

Solution 19

Solution 20

Solution 21

Solution 22

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Solution 26

Exercise Ex. 6.2

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Solution 2

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Solution 10

Exercise Ex. 6.3

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Solution 4

x + y ≥ 4   … (1)

2x – y < 0  … (2)

The graph of the lines, x + y = 4 and 2x – y = 0 are drawn in the figure below.

Inequality (1) represents the region above the line x + y = 4. (including the line x + y = 4)

It is observed that (–1, 0) satisfies the inequality, 2x – y < 0.

[2(-1) – 0 = -2< 0]

Therefore, inequality (2) represents the half plane corresponding to the line, 2x – y = 0 containing the point (-1, 0). [excluding the line 2x – y < 0]

Hence, the solution of the given system of linear inequalities is represented by the common shaded region including the points on the line x + y = 4 and excluding the points on line 2x – y = 0 as follows:

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Exercise Misc. Ex.

Solution 1

Solution 2

Solution 3

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Solution 10

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Solution 12

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Solution 14

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