Solve the given inequalities $3 x+2 y \geq 24,3 x+y \leq 15, x \geq 4$, graphically in two - dimensional plane.
The graphical representation of $3 x+2 y \geq 24,3 x+y \leq 15$
$x \geq 4$ is given by common region in the figure below.
$3 x+2 y \geq 24 \ldots \ldots$ (1)
$3 x+y \leq 15 \ldots \ldots$ (2)
$x \geq 4 \ldots \ldots$ (3)
Inequality (1) represents the region above line $3 x+2 y=24$ (including the line $3 x+2 y=24$ ).
Inequality $(2)$ represents the region below line $3 x+y=15$ (including the line $3 x+y=15$ ).
Inequality (3) represents the region in front of line $x=4$ (including the line $x=4$ ).
Therefore, we can see in the figure that there is no common shaded region.
So there linear inequalities in equations has no solution.
This can be represented as follows,
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