The solution set for the system of linear ine | vedclass

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(A) The system of linear inequalities is given by:$1) x+y \geq 1$$2) 7x+9y \leq 63$$3) y \leq 5$$4) x \leq 6$$5) x \geq 0, y \geq 0$To find the feasib

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(A) The system of linear inequalities is given by:$1) x+y \geq 1$$2) 7x+9y \leq 63$$3) y \leq 5$$4) x \leq 6$$5) x \geq 0, y \geq 0$To find the feasible region,we analyze the boundaries:- The line $x+y=1$ passes through $(1,0)$ and $(0,1)$. The region $x+y \geq 1$ is away from the origin.- The line $7x+9y=63$ passes through $(9,0)$ and $(0,7)$. The region $7x+9y \leq 63$ is towards the origin.- The lines $x=6$ and $y=5$ are vertical and horizontal lines respectively,bounding the region.- The conditions $x \geq 0$ and $y \geq 0$ restrict the region to the first quadrant.By plotting these lines and considering the inequalities,the feasible region is the bounded polygon in the first quadrant that satisfies all conditions. Comparing this with the provided options,the figure in the solution image (which matches option $A$) correctly represents the intersection of all these half-planes.

The solution set for the system of linear inequations $x+y \geq 1$,$7x+9y \leq 63$,$y \leq 5$,$x \leq 6$,$x \geq 0$,and $y \geq 0$ is represented graphically. Which of the following figures represents the correct solution set?

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