Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\ge -\frac{2}{3}x+2\\ y>2x-3\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations and the graph is

Step-by-step solution

Given information 

Given system of equations$\left\{\begin{array}{l}y\ge -\frac{2}{3}x+2\\ y>2x-3\end{array}\right.$

Checking the point for system of equation 

The equation $y=-\frac{2}{3}x+2$has intercept $2,3$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0\ge 0+2 \\ 0\ge 2 \end{gathered}$$which is not true

So origin is not included

Checking the point for system of equations

The equation $y=2x-3$has intercept $-3,\frac{3}{2}$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0>0-3 \\ 0>-3 \end{gathered}$$which is not true

So origin is not included

Graphing the system of equations

The graph of the system of equations is