Chapter 6.6, Problem 39HP

To determine

To find:Whether theSystem of inequalities have parallel boundaries have no solution .

Answer to Problem 39HP

Given statement is sometimes True.

Explanation of Solution

Let us assume a system of inequalities they are

  $\begin{array}{l}3x-2y>5\\ 3x-2y<1\end{array}$

Graph of above inequalities is

  

Here

Red colour represents the region of inequality $3x-2y>5$

Blue colour represents the region of inequality $3x-2y<1$

As there is no common region of Red and Blue colour.

It means that there is no solution.

Let us consider another system of inequalities

  $\begin{array}{l}x\le 3\\ x\le 1\end{array}$

Graph of above inequalities is

  

Here

Blue colour represents the region of inequality $x\le 1$

Red colour represents the region of inequality $x\le 3$ .

The common region of Red colour and Blue colour represents the Solution of above inequalities.

Therefore

It is sometimes true that systems with parallel boundaries have no solution. It is also possible that the solution could be one of the regions determined by the parallel boundaries.