The common region of the solution of the ineq | vedclass

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(D) To find the common region,we analyze the given inequations:$1$. $x+y \geq 5$: This represents the region on or above the line $x+y=5$. Since $(0,0

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bounded and non-origin side

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(D) To find the common region,we analyze the given inequations:$1$. $x+y \geq 5$: This represents the region on or above the line $x+y=5$. Since $(0,0)$ does not satisfy this ($0 \geq 5$ is false),the region is on the non-origin side.$2$. $y \leq 4$: This represents the region on or below the line $y=4$.$3$. $x \geq 2$: This represents the region on or to the right of the line $x=2$.$4$. $x, y \geq 0$: This restricts the region to the first quadrant.By plotting these lines,we observe the shaded region in the figure. The region is bounded by the lines $x=2$,$y=4$,and $x+y=5$. Since the region is enclosed by these lines,it is a bounded region. Furthermore,the origin $(0,0)$ does not lie in the shaded region,so it is on the non-origin side.Therefore,the correct option is $D$.

The common region of the solution of the inequations $x+y \geq 5$,$y \leq 4$,$x \geq 2$,$x, y \geq 0$ is

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