Question

In the following exercises, solve each system by graphing$\left\{\begin{array}{l}3x-y\ge 6\\ y\ge -\frac{1}{2}x\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equation

Step-by-step solution

Given information 

Given the system of equations$\left\{\begin{array}{l}3x-y\ge 6\\ y\ge -\frac{1}{2}x\end{array}\right.$

Checking the point for the system of equations

The equation $3x-y=6$has intercept $-6,2$. Testing the point $(0,0)$, we get

$$\begin{gathered} 3\left(0\right)-0\ge 6 \\ 0-0\ge 6 \\ 0\ge 6 \end{gathered}$$which is not true

So origin is not included

Checking for another equation

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

$$\begin{gathered} 0\ge -\frac{1}{2}\left(0\right) \\ 0\ge 0 \end{gathered}$$which is true

So origin is included

Graphing the equation

The graph of the equation is