# Solve the given inequalities x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0,graphically in two – dimensional plane.

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Solve the given inequalities x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0,graphically in two – dimensional plane.

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The graphical representation of x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0 is given by common region in the figure below.

x + 2y ≤ 10 ..... (1)

x + y ≥ 1 ..... (2)

y ≥ 0 ...... (3)

y ≥ 0 ...... (4)

x – y ≤ 0 ...... (5)

Inequality (1) represents the region below line x + 2y = 10 (including the line x + 2y = 10).

Inequality (2) represents the region above line x + y = 11 (including the line x + y = 11).

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 above line x - y = 0 (including the line x - y = 0).

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,