Chapter 6.6, Problem 47PFA

To determine

To find: Which of the following is not a correct description of the graph of the system.

Answer to Problem 47PFA

Option C

Explanation of Solution

Given information:

  $\begin{array}{l}-6x+2y\ge 5\\ y<3x+2\end{array}$ .

Graph of given inequalities is

  

Here red colour represents the region of inequality $-6x+2y\ge 5$

Blue colour represents the region of inequality $y<3x+2$

As both lines are parallel and there is no common region of Red and Blue colors.

So, there is no solution.

So, Option C is incorrect The solution of the system is area between the two lines is incorrect.

Substitute $\left(-3,6\right)$ in the inequality $-6x+2y\ge 5$

We get

  $\begin{array}{l}-6x+2y\ge 5\\ \Rightarrow -6\left(-3\right)+2\left(6\right)\ge 5\\ \Rightarrow 18+12\ge 5\\ \Rightarrow 30\ge 5\end{array}$

Which is True.

So, Point $\left(-3,6\right)$ lies in region of $-6x+2y\ge 5$

Substitute $\left(2,5\right)$ in the inequality $y<3x+2$

We get

  $\begin{array}{l}y<3x+2\\ \Rightarrow 5<3\left(2\right)+2\\ \Rightarrow 5<6+2\\ \Rightarrow 5<8\end{array}$

Which is True

So, Point $\left(2,5\right)$ lies in the region of $y<3x+2$ .

So, Option C is incorrect.