91Ó°ÊÓ

The given system is$\left\{\begin{array}{l}2x-5y<10\\ 3x+4yâ‰\yen 12\end{array}\right.$.

• To plot the inequality $2x-5y<10$, draw the dashed line $2x-5y=10$because the inequality sign does not include equality.
• The point $(0,0)$ satisfies the inequality, so shade the region that includes the origin.

• To plot the inequality $3x+4yâ‰\yen 12$, draw the solid line $3x+4y=12$because the inequality sign includes equality.
• The point $(0,0)$ does not satisfies 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 $(5,5)$.
• Check if the point satisfies the inequalities.

$$\begin{gathered} 2\left(5\right)-5\left(5\right)\stackrel{?}{<}10 \\ 10-25\stackrel{?}{<}10 \\ -15<10 \\ 3\left(5\right)+4\left(5\right)\stackrel{?}{â‰\yen }12 \\ 15+20\stackrel{?}{â‰\yen }12 \\ 35â‰\yen 12 \end{gathered}$$

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