# Solve the given inequalities 3x + 2y ≤ 12, x ≤ 1, y ≥ 2graphically in two – dimensional plane.

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Solve the given inequalities 3x + 2y ≤ 12, x ≤ 1, y ≥ 2graphically in two – dimensional plane.

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The graphical representation of 3x + 2y ≤ 12, x ≤ 1, y $\ge$2  is given by common region in the figure below.

3x + 2y ≤ 12 ...... (1)

x ≤ 1 ...... (2)

$\ge$2 ..... (3)

Inequality (1) represents the region below line 3x + 2y = 12 (including the line).

Inequality (2) represents the region behind line x = 1 (including the line x=1).

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

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,