The solution set of the inequation 2x + y > 5 is
(a) half plane that contains the origin
(b) open half plane not containing the origin
(c) whole xy-plane except the points lying on the line 2x + y = 5
(d) none of these

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Solution

(b) open half plane not containing the origin

On putting x = 0, y = 0 in the given inequality, we get
0 > 5, which is absurd.

Therefore, the solution set of the given inequality does not include the origin.

Thus, the solution set of the given inequality consists of the open half plane not containing the origin.

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y \geq 2 x + 1

y > \frac{1}{2} x - 1

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\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z - 1}{3}

2 x + 3 y - z = 5

L : \frac{x + 1}{- 1} = \frac{y}{2} = \frac{z - 1}{3}

π : x - 2 y + z = 6

π

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\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z - 1}{3}

2 x + 3 y - z = 5

x + y + z - 6 = 0

2 x + 3 y + z + 5 = 0

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