Chapter 6.6, Problem 5LC

To determine

To explain: that the system has no solution.

Answer to Problem 5LC

Explanation of Solution

Given information:

A graphing system of two linear inequalities and the boundary lines for the inequalities are parallel.

Calculation:

Let consider the system of inequalities,

  $\begin{array}{l}y<2x+\mathrm{4.............}(1)\\ 2x-y\le \mathrm{4.............}(2)\end{array}$

The boundaries of these inequalities are parallel. Verify whether they have common solution or not.

Graph of $y<2x+4$ and $2x-y\le 4$ is shown below:

  

The region with squares represents solutions of both inequalities. The system solutions lie in the region with square where the graphs overlap.

The solutions of the system are all of the points in the shaded region, including the points on the solid boundary lines.

Therefore, it is not essential, as long as there is some overlap of the half planes, and then the system will have a solution.