Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le -\frac{2}{3}x+5\\ x\ge 3\end{array}\right.$

Short answer

The darkest region is the solution to the system of equations.

Step-by-step solution

Given information 

Given system of equations

$\left\{\begin{array}{l}y\le -\frac{2}{3}x+5\\ x\ge 3\end{array}\right.$

Graph the system of equations 

The system of equations $y=-\frac{2}{3}x+5$ has intercept $x=7.5,y=5$ The boundary is solid.

Calculating for second equation 

For $x\ge 3$, the intercepts are $x=3,y=0$and testing the point $(0,0)$, we get

$0\ge 3$which is false hence, origin is not contained in it.

Plotting the graph