Question

In the following exercises, solve each system by graphing.

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

Short answer

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

Step-by-step solution

Given information 

Given the system of equations $\left\{\begin{array}{l}y<2x-1\\ y\le -\frac{1}{2}x+4\end{array}\right.$

Graph the system of equations 

The equation$y=2x-1$has intercepts as $-1,\frac{1}{2}$. Testing the point $0,0$, we get

$$\begin{gathered} 0<0-1 \\ 0<-1 \end{gathered}$$which is not true so origin is not included

Checking for another equation 

The equation $y=-\frac{1}{2}x+4$has intercept $4,8$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0\le 0+4 \\ 0\le 4 \end{gathered}$$which is true so origin is included

Graphing the equation 

The graph of the equation is