Q 292 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing$\left\{\begin{array}{l}3x-y\ge 6\\ y\ge -\frac{1}{2}x\end{array}\right.$

Step-by-Step Solution

Answer

The darkest region represent the solution to the system of equation

Step 1: Given information

Given the system of equations $\left\{\begin{array}{l}3x-y\ge 6\\ y\ge -\frac{1}{2}x\end{array}\right.$

Step 2: Checking the point for the system of equations

The equation $3 x-y=6$ has intercept $-6,2$. Testing the point $(0,0)$, we get

$$\begin{gathered} 3\left(0\right)-0\ge 6 \\ 0-0\ge 6 \\ 0\ge 6 \end{gathered}$$ which is not true

So origin is not included

Step 3: Checking for another equation

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

$$\begin{gathered} 0\ge -\frac{1}{2}\left(0\right) \\ 0\ge 0 \end{gathered}$$ which is true

So origin is included

Step 4: Graphing the equation

The graph of the equation is