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(C) The given system of inequations is $x \geq 0$,$y \geq 0$,$y \leq 6$,and $x+y \leq 3$.$1$. The conditions $x \geq 0$ and $y \geq 0$ restrict the re

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bounded in first quadrant

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(C) The given system of inequations is $x \geq 0$,$y \geq 0$,$y \leq 6$,and $x+y \leq 3$.$1$. The conditions $x \geq 0$ and $y \geq 0$ restrict the region to the first quadrant.$2$. The line $x+y = 3$ passes through $(3, 0)$ and $(0, 3)$. The inequality $x+y \leq 3$ represents the region on or below this line.$3$. The condition $y \leq 6$ is satisfied by the region defined by $x+y \leq 3$ in the first quadrant,as the maximum value of $y$ in this region is $3$.$4$. Since the region is enclosed by the axes and the line $x+y=3$,it is a bounded region in the first quadrant.

The region represented by the inequation system $x, y \geq 0, y \leq 6, x+y \leq 3$ is

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