Q. 286 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing.  

$\left\{\begin{array}{l}y\le 3x+2\\ y>x-1\end{array}\right.$

Step-by-Step Solution

Answer

The darkest region is the solution to the system of equations and the graph is 

Step 1: Given information

Given the system of equations  $\left\{\begin{array}{l}y\le 3x+2\\ y>x-1\end{array}\right.$

Step 2: Graph the system of equations

The system of equations $y=3x+2$ has intercept  The boundary is solid. Testing the point , $(0,0)$we get

$$\begin{gathered} 0\le 0+2 \\ 0\le 2 \end{gathered}$$ which is true

Step 3: Calculating for second equation

For $y=x-1$, the intercepts are $-1,1$ and testing the point $(0,0)$, we get

$$\begin{gathered} 0>0-1 \\ 0>-1 \end{gathered}$$ which is true

So both of them contains the origin 

Step 4: Plotting the graph

The graph is