Question:
Solve the given inequalities $x \geq 2 y, y \geq 3$ graphically in two-dimensional plane.
Solution:
The graphical representation of $x \geq 2 y, y \geq 3$ is given by common region in the figure below.
$x \geq 2 y \ldots \ldots(1)$
$y \geq 3 \ldots \ldots(2)$
Inequality (1) represents the region below line $x=2 y$ (including the line $x=2 y$ ).
Inequality $(2)$ represents the region above line $y=3($ including the line $y=3)$.
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,
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