Question

The darkest region represent the solution to the system of equations $\left\{\begin{array}{l}x+2y<4\\ y<x-2\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

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

Checking the point for the system of equations

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

$$\begin{gathered} 0+0<4 \\ 0<4 \end{gathered}$$which is true

So origin is included

Checking for another equation

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

$$\begin{gathered} 0<0-2 \\ 0<-2 \end{gathered}$$which is not true

So origin is not included

Graph of system of equation

The graph is