Q 293 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

The darkest region represent the solution to the system of equations

Step 1: Given information

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

Step 2: Checking the point

The equation, $2 x+4 y=8$ 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

Step 3: 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

Step 4: Sketching the graph

The graph is