Q 308 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

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

Step-by-Step Solution

Answer

The equations have no solution.  

Step 1: Given information.

Given system of equation 

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

Step 2: 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.

Step 3: 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.

Step 4: Plotting the graph