Chapter 6.6, Problem 41HP

To determine

To find: Second inequality of the system such that there is no solution .

Answer to Problem 41HP

  $3x-y<-4$

Explanation of Solution

Given information:

One of the inequality of the system is $3x-y>4$ .

Condition for no solution is that graphs of both inequalities should not overlap.

Let 1st inequality $3x-y>4$ represents the region in one direction. And the 2nd inequality $3x-y<-4$ represents the region in another direction (opposite to the 1^st). As both graphs are in opposite direction there will be any common region. So there will be no solution.

  

Here

Blue colour represents the region of inequality $3x-y<-4$ .

Red colour represents the region of inequality $3x-y>4$

As there is no common region so there in no solution.