Q 310 - Intermediate Algebra

Question

In the following exercises, solve each system by graphing.

$\left\{\begin{array}{l}-2x+6y<0\\ 6y>2x+4\end{array}\right.$  

Step-by-Step Solution

Answer

The equations have no solution. 

Step 1: Given information.

Given system of equation, 

$\left\{\begin{array}{l}-2x+6y<0\\ 6y>2x+4\end{array}\right.$

Step 2: Graph the system of equations

The system of equation $-2x+6y=0$ 

has intercept $x=0,y=0$. The boundary is solid. Origin does not lies within as putting

$$\begin{gathered} (0,0) \\ 0<0 \end{gathered}$$

which holds false.

Step 3: Calculating for second equation

For $6y>2x+4$,

the intercepts are $x=-2,y=0.6$ and testing the point $(0,0)$,

we get

$0>4$,

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

Step 4: Plotting the graph.