Question

In the following exercises, solve each system by graphing$\left\{\begin{array}{l}3x-2y\le 6\\ -4x-2y>8\end{array}\right.$

Short answer

The darkest region represent the solution to the system of equations

Step-by-step solution

Given information

Given the system of equations$\left\{\begin{array}{l}3x-2y\le 6\\ -4x-2y>8\end{array}\right.$

Checking the point

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

$$\begin{gathered} 3\left(0\right)-2\left(0\right)\le 6 \\ 0-0\le 6 \\ 0\le 6 \end{gathered}$$which is true

So origin is included

Checking for another equation

The equation, $-4x-2y=8$has the intercept localid="1659017030170" $-4,-2$. Testing the point (0,0), we get

$$\begin{gathered} -4\left(0\right)-2\left(0\right)<8 \\ 0-0<8 \\ 0<8 \end{gathered}$$which is true

So origin is included

Graphing the equation

The graph is