Q. 300 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing  $\left\{\begin{array}{l}y\ge -\frac{1}{2}x-3\\ x\le 2\end{array}\right.$

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

Step 2: Checking the point for the equations

The equation $y=-\frac{1}{2}x-3$ has the intercept $-3,-1.5$. Testing the point $(0,0)$, we get

$$\begin{gathered} 0\ge -0.5\left(0\right)-3 \\ 0\ge 0-3 \\ 0\ge -3 \end{gathered}$$ which is true

So origin is included

Step 3: Checking for another equation

The equation $x\le -2$ .Testing the point $(0,0)$, we get

$0\le -2$ which is not true so origin is not included

Step 4: Sketching the graph

The graph is