Q 313 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

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

Step-by-Step Solution

Answer

The solution is the dark shaded region.

Step 1: Given information.

Given system of equation, 

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

Step 2: 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.

Step 3: 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.

Step 4: Plotting the graph.