Question

In the following exercises, solve each system by graphing,$\left\{\begin{array}{l}2x+2y>-4\\ -x+3y\ge 9\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}2x+2y>-4\\ -x+3y\ge 9\end{array}\right.$

Checking the point for the system of equation

The equation is, $2x+2y=4$,the intercept is $2,2$. Checking the point $(0,0)$, we get

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

So origin is included

Checking for another equation

The equation, $-x+3y=9$has the intercept $3,-9$. Testing the point $(0,0)$, we get

$$\begin{gathered} -0+3\left(0\right)\ge 9 \\ 0+0\ge 9 \\ 0\ge 9 \end{gathered}$$which is not true

So origin is not included

Graphing the equation

The graph is