Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}-3x+6y\ge 12\\ 4y\le 2x-4\end{array}\right.$

Short answer

The equations have no solution.

Step-by-step solution

Given information.   

Given system of equation,

$\left\{\begin{array}{l}-3x+6y\ge 12\\ 4y\le 2x-4\end{array}\right.$

Graph the system of equations  

The system of equation $-3x+6y=12$

has intercept $x=-4,y=2$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0\ge 12 \end{gathered}$$

which holds false.

Calculating for second equation  

For $4y=2x-4$,

the intercepts are $x=2,y=-1$and testing the point ,

we get

$0\le -4$,

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

Plotting the graph.