91Ó°ÊÓ

Consider the first inequality in the system of inequalities is $xâ‰\yen 0$& $yâ‰\yen 0$.

$x+2yâ‰\yen 1$equation of the equality consider by replacing with equality $x+2y=1$

For determining the shaded portion we use to test a point with $(0,0)$

$$\begin{gathered} 0+0â‰\yen 1 \\ 0â‰\yen 1 \end{gathered}$$

$x+2y≤10$,the equation of line is replacing by inequality with equality$x+2y=10$

By substituting by test point $(0,0)$

$$\begin{gathered} 0+0≤10 \\ 0≤10 \end{gathered}$$

The point $(0,0)$contains the shaded portion in the equation $x+2y≤10$

$x+yâ‰\yen 2$, the equation of line replacing with equality $x+y=2$

By using the testing point $(0,0)$

$$\begin{gathered} 0+0â‰\yen 2 \\ 0â‰\yen 2 \end{gathered}$$

The point$(0,0)$does not includes with the inequality$x+yâ‰\yen 2$

$x+y≤8$,the equation of line replace with equality $x+y=8$

By using test point$(0,0)$

$0+0≤8$

role="math" localid="1646922749498" $0≤8$

The point $(0,0)$includes the inequality$x+y≤8$

The shaded portion is the bounded region: