Q. 4.114 - Intermediate Algebra

Question

Solve the system by graphing: 

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

Step-by-Step Solution

Answer

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

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 &#160; + &#160; 3 y &#160; &#62; &#160; 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 &#60; - 1 3 x - 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.