Q 295 - Intermediate Algebra

Question

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

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

Step 2: Checking the point

The equation, $3 x-2 y=6$ 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

Step 3: Checking for another equation

The equation, $-4 x-2 y=8$ has the intercept $-4,-2$. 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

Step 4: Graphing the equation

The graph is