Q. 299 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing $\left\{\begin{array}{l}x-3y>4\\ y\le -1\end{array}\right.$

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 $\left\{\begin{array}{l}x-3y>4\\ y\le -1\end{array}\right.$

Step 2: Checking the point for the equations

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

$$\begin{gathered} 0-3\left(0\right)>4 \\ 0-0>4 \\ 0>4 \end{gathered}$$ which is not true

So the origin is not included

Step 3: Checking for another equation

The equation is $y\le -1$. Testing the point $(0,0)$ , we get

$0\le -1$ which is not true

So origin is not included

Step 4: Graph the system of equations

The graph is