Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}y\ge -\frac{1}{2}x-3\\ x\le 2\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}y\ge -\frac{1}{2}x-3\\ x\le 2\end{array}\right.$

Checking the point for the equations 

The equation $y=-\frac{1}{2}x-3$has the intercept $-3,-1.5$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0\ge -0.5\left(0\right)-3 \\ 0\ge 0-3 \\ 0\ge -3 \end{gathered}$$which is true

So origin is included

Checking for another equation

The equation $x\le -2$.Testing the point $(0,0)$, we get

$0\le -2$which is not true so origin is not included

Sketching the graph

The graph is