# Solve the given inequalities x – 2y ≤ 2, x + y ≥ 3, –2x + y ≤ 4, x ≥ 0, y ≥ 0 graphically in two – dimensional plane.

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Solve the given inequalities x – 2y ≤ 2, x + y ≥ 3, –2x + y ≤ 4, x ≥ 0, y ≥ 0 graphically in two – dimensional plane.

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The graphical representation of x – 2y ≤ 2, x + y ≥ 3, –2x + y ≤ 4, x ≥ 0, y ≥ 0 is given by common region in the figure below.

x – 2y ≤ 2 ....... (1)

x + y ≥ 3 ........ (2)

x ≥ 0 ......... (3)

y ≥ 0 ........ (4)

–2x + y ≤ 4 ........ (5)

Inequality (1) represents the region above line x – 2y = 2 (including the line x – 2y = 2).

Inequality (2) represents the region above line x + y = 3 (including the line x + y = 3).

Inequality (3) represents the region in front of line x = 0 (including the line  x = 0).

Inequality (4) represents the region above line y = 0 (including the line y = 0).

Inequality (5) represents the region below line -2x + y = 4 (including the line -2x + y = 4).

Therefore, every point in the common shaded region including the points on the respective lines represents the solution for the given inequalities.

This can be represented as follows, 