Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}y\le 3x+2\\ y>x-1\end{array}\right.$

Short answer

The darkest region is the solution to the system of equations and the graph is

Step-by-step solution

Given information

Given the system of equations $\left\{\begin{array}{l}y\le 3x+2\\ y>x-1\end{array}\right.$

Graph the system of equations 

The system of equations $y=3x+2$has intercept The boundary is solid. Testing the point , $(0,0)$we get

$$\begin{gathered} 0\le 0+2 \\ 0\le 2 \end{gathered}$$which is true

Calculating for second equation 

For $y=x-1$, the intercepts are $-1,1$and testing the point $(0,0)$, we get

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

So both of them contains the origin

Plotting the graph 

The graph is