Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}2x+4y>4\\ y\le -\frac{1}{2}x-2\end{array}\right.$

Short answer

The equations have no solution.

Step-by-step solution

Given information.

Given system of equation

$\left\{\begin{array}{l}2x+4y>4\\ y\le -\frac{1}{2}x-2\end{array}\right.$

Graph the system of equations   

The system of equations $2x+4y=4$has intercept $x=2,y=1$.The boundary is solid. Origin does not lies within as putting $$\begin{gathered} (0,0) \\ 0\ge 4 \end{gathered}$$

which holds false.

Calculating for second equation   

For $y=-\frac{1}{2}x-2$,

the intercepts are $x=-4,y=-2$and testing the point $(0,0)$, we get

$0\le -2$,

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

Plotting the graph