Show that the solution set of the following system of linear inequalities is an unbounded region: $2x + y \geq 8$,$x + 2y \geq 10$,$x \geq 0$ and $y \geq 0$.

(N/A) Solution:
We have the system of linear inequalities: $2x + y \geq 8$,$x + 2y \geq 10$,$x \geq 0$,and $y \geq 0$.
$1$. The line $2x + y = 8$ passes through the points $(0, 8)$ and $(4, 0)$.
$2$. The line $x + 2y = 10$ passes through the points $(0, 5)$ and $(10, 0)$.
$3$. For the origin $(0, 0)$,we test the inequalities:
- For $2x + y \geq 8$: $2(0) + 0 = 0 < 8$. Thus,the origin does not satisfy the inequality,and the region lies on the side of the line away from the origin.
- For $x + 2y \geq 10$: $0 + 2(0) = 0 < 10$. Thus,the origin does not satisfy the inequality,and the region lies on the side of the line away from the origin.
$4$. The conditions $x \geq 0$ and $y \geq 0$ restrict the solution to the first quadrant.
$5$. By plotting these lines and identifying the common region satisfying all inequalities,we observe that the shaded region extends infinitely away from the origin.
$6$. Therefore,the solution set is an unbounded region.