91Ó°ÊÓ

The given system is$\left\{\begin{array}{l}3x-2y≤6\\ y>-\frac{1}{4}x+5\end{array}\right.$.

• The intercepts of $3x-2y=6$are $(2,0),(0,3)$.
• Join the points to plot a solid line.
• The point localid="1647926954853" $(0,0)$satisfies the inequality, so shade the region that includes the origin.

• The intercepts of $y=\frac{-1}{4}x+5$are $(0,5),(20,0)$.
• Join the points to plot a dotted line.
• The point$(0,0)$ satisfies the inequality, so shade the region that includes the origin.

• The solution set is the region shaded with the darker color excluding the point of intersection as it does not satisfy the second inequality.

• One of the points that lie in the solution set is $(0,6)$.
• Check if the point satisfies the inequalities.

$$\begin{gathered} 3\left(0\right)-2\left(6\right)\stackrel{?}{≤}6 \\ -12≤6 \end{gathered}$$

$$\begin{gathered} 6\stackrel{?}{>}-\frac{1}{4}\left(0\right)+5 \\ 6>5 \end{gathered}$$

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