Chapter 5.7, Problem 47E

To determine

To find: the system of linear inequalities that has exactly one solution.

Answer to Problem 47E

The system of linear inequalities with exactly one solution are given and the graph is drawn.

Explanation of Solution

Given:

A system of linear inequalities that has exactly one solution.

Concept used:

For a system of linear inequalities that has exactly one solution.

It means the system of inequalities must have only one point in the intersection of graphs of inequalities.

Graphing the inequalities, it will graph the ordinary linear functions just like it is done before. The difference is that a solution to the inequality is not the drawn line but the area of the coordinate plane that satisfy the inequality. the boundary line is dashed for $<\text{or >}$ and solid line for $\le \text{or }\ge$ The common area is the solution of inequality.

Calculation:

Write the system of linear inequalities that has exactly one solution in the solution set.

It means the system of inequalities must have only one point in the intersection of graphs of inequalities.

Consider the below inequalities.

  $\begin{array}{l}y\ge 3.\\ y\le 3.\\ x\ge 2.\\ x\le 2.\end{array}$

Graph the given system of linear inequalities.

  $y\ge 3,y\le 3,x\ge 2\text{ and }x\le 2.$ as shown in the below figure. The order pair:

  $\left(x,y\right)=\left(2,3\right)$ is the only one solution in the solution set.

The graph of the inequalities $y\ge 3,y\le 3,x\ge 2\text{ and }x\le 2$ :

Hence, the system of linear inequalities with exactly one solution are given and there graph is drawn.