Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}-2x+6y<0\\ 6y>2x+4\end{array}\right.$

Short answer

The equations have no solution.

Step-by-step solution

Given information.  

Given system of equation,

$\left\{\begin{array}{l}-2x+6y<0\\ 6y>2x+4\end{array}\right.$

Graph the system of equations  

The system of equation $-2x+6y=0$

has intercept $x=0,y=0$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0<0 \end{gathered}$$

which holds false.

Calculating for second equation   

For $6y>2x+4$,

the intercepts are $x=-2,y=0.6$and testing the point $(0,0)$,

we get

$0>4$,

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

Plotting the graph.