91Ó°ÊÓ

The given system is$\left\{\begin{array}{l}yâ‰\yen -3x+2\\ 3x+y>5\end{array}\right.$.

• To plot the inequality $yâ‰\yen -3x+2$, draw the solid line $y=-3x+2$because the inequality sign includes equality.
• The point $(0,0)$does not satisfy the inequality, so shade the region that does not include the origin.

• To plot the inequality $3x+y>5$, draw the dotted line $3x+y=5$because the inequality sign does not include equality.
• The point $(0,0)$does not satisfy the inequality, so shade the region that does not include the origin.

• The solution set is the region shaded with a darker color.

• One of the points that lie in the solution set is $(2,0)$.
• Check if the point satisfies the inequalities.

$$\begin{gathered} 0\stackrel{?}{â‰\yen }-3\left(2\right)+2 \\ 0\stackrel{?}{â‰\yen }-6+2 \\ 0â‰\yen -4 \\ 3\left(2\right)+0\stackrel{?}{>}5 \\ 6>5 \end{gathered}$$

• As both the inequalities are satisfied, the solution is verified.