Question

In the following exercises, solve each system by graphing.

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

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

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

Checking the point for the system of equations

The equation $x-y=1$has intercept $-1,1$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0-0>1 \\ 0>1 \end{gathered}$$

So origin is not included

Checking for the another system of equation

The equation$y=-\frac{1}{4}x+3$has intercept $3,12$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0<0+3 \\ 0<3 \end{gathered}$$which is true

So origin is included

Graphing the equation

The graph of the equations is