Answer
See graph
Work Step by Step
Given $$\begin{cases}
4 x-6 y & >3 \\
y & >-2 x+5.
\end{cases}$$ Rewrite the first inequality so that $y$ is a function of $x$.
\begin{equation}
\begin{aligned}
4 x-6 y &> 3\\
-6y&> 3-4 x\\
6y&< 4 x-3\\
y&< \frac{4}{6}x-\frac{3}{6}\\
y& <\frac{2}{3}x-\frac{1}{2}.
\end{aligned}
\end{equation} Now, graph the following functions with a dashed line each and shade the appropriate areas where the inequalities are satisfied.
\begin{equation}
\begin{aligned}
y&=-2 x+5\\
y&=\frac{2}{3}x-\frac{1}{2}\\
\end{aligned}
\end{equation} See the graph below. The set of inequality is satisfied in the region between the two graphs.
