Question

Solve the system by graphing:

$\left\{\begin{array}{l}x+3y>8\\ y<-\frac{1}{3}x-2\end{array}\right.$

Short answer

There is no solution to this system of inequalities as there is no common region between the inequalities in the below graph.

Step-by-step solution

Step 1. Given information  

The given system of inequalities is:

$\left\{\begin{array}{l}x+3y>8\\ y<-\frac{1}{3}x-2\end{array}\right.$

Step 2. Graph the inequality  x + 3y > 8

We will graph the inequality by graphing $x+3y=8$and the boundary will be a dashed line because it contains greater than sign.

The graph is given as:

Step 3. Graph of the inequality y<-13x-2

We will graph the inequality by graphing $y=\frac{-1}{3}x-2$on the same cartesian plane and the boundary line will be a dashed line since it contains less than sign.

The graph is given as:

There is no solution to this system of inequalities as there is no common region between the inequalities in the above graph.