Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}2x+4y\ge 8\\ y\le \frac{3}{4}x\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

Given the system of equations $\left\{\begin{array}{l}2x+4y\ge 8\\ y\le \frac{3}{4}x\end{array}\right.$

Checking the point

The equation, $2x+4y=8$has the intercept $2,4$. Testing the point $(0,0)$, we get

$$\begin{gathered} 2\left(0\right)+4\left(0\right)\ge 8 \\ 0+0\ge 8 \\ 0\ge 8 \end{gathered}$$which is not true

So origin is not included

Checking for another point

The equation, $y=\frac{3}{4}x$Testing the point $(0,0)$, we get

$$\begin{gathered} 0\le \frac{3}{4}\left(0\right) \\ 0\le 0 \end{gathered}$$which is true

So origin is included

Sketching the graph

The graph is