Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}x-3y\ge 6\\ y>\frac{1}{3}x+1\end{array}\right.$

Short answer

The equations have no solution.

Step-by-step solution

Given information. 

Given system of equation,

$\left\{\begin{array}{l}x-3y\ge 6\\ y>\frac{1}{3}x+1\end{array}\right.$

Graph the system of equations 

The system of equation $x-3y=6$

has intercept $x=6,y=-2$.The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0\ge 6 \end{gathered}$$

which holds false.

Calculating for second equation    

For $y=\frac{1}{3}x+1$,

the intercepts are $x=-3,y=1$and testing the point $(0,0)$,

we get

$0>1$,

which is false hence, the origin is not contained in it.

Plotting the graph.