Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}2x+y>-6\\ -x+2y\ge -4\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}2x+y>-6\\ -x+2y\ge -4\end{array}\right.$

Checking the point

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

$$\begin{gathered} 2\left(0\right)+0>-6 \\ 0+0>-6 \\ 0>-6 \end{gathered}$$which is true

So origin is included

Checking for another equation

The equation $-x+2y=-4$has intercept $-2,4$.Testing the point $(0,0)$, we get

$$\begin{gathered} -0+2\left(0\right)\ge -4 \\ 0+0\ge -4 \\ 0\ge -4 \end{gathered}$$which is true

So origin is included

Sketching the graph

The graph is