Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y<-2x+2\\ y\ge -x-1\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

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

Graph the system of equations 

The system of equations $y=-2x+2$has the intercept as $1,2$. Testing the point $(0,0)$, we get

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

Checking for another equation

The equation $y=-x-1$has intercept as $-1,1$and the testing point $(0,0)$has

$$\begin{gathered} 0\ge 0-1 \\ 0\ge -1 \end{gathered}$$ which is true

Step 4

The graph for the system of equation is