Question

In the following exercises, solve each system by graphing.

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

Short answer

The solution is the dark shaded region.

Step-by-step solution

Given information.   

Given system of equation,

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

Graph the system of equations   

The system of equation $y=\frac{1}{2}x-1$

has intercept $x=2,y=-1$. The boundary is solid. Origin does lies within as putting

$0\ge -1$

which holds true.

Calculating for second equation    

For $-2x+4y=4$,

the intercepts are $x=-2,y=1$and $(0,0)$testing the point ,

we get

$0\ge 4$,

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

Plotting the graph.