Q 311 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing. 

$\left\{\begin{array}{l}-3x+6y\ge 12\\ 4y\le 2x-4\end{array}\right.$

Step-by-Step Solution

Answer

The equations have no solution.  

Step 1: Given information.

Given system of equation, 

$\left\{\begin{array}{l}-3x+6y\ge 12\\ 4y\le 2x-4\end{array}\right.$

Step 2: Graph the system of equations

The system of equation $-3x+6y=12$ 

has intercept $x=-4,y=2$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0\ge 12 \end{gathered}$$

which holds false.

Step 3: Calculating for second equation

For $4y=2x-4$,

the intercepts are $x=2,y=-1$ and testing the point ,

we get

$0\le -4$,

which is false hence, the origin is not contained in it.

Step 4: Plotting the graph.