Q 288 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing.  

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

Step-by-Step Solution

Answer

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

Step 1 : Given information

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

Step 2: Graph the system of equations

The equation$y=2 x-1$ 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

Step 3: 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

Step 4: Graphing the equation

The graph of the equation is