Chapter 5, Problem 7CT

To determine

To find: the system of linear inequalities having some point as solution and other as not solution.

Answer to Problem 7CT

The graph of system of linear inequalities is drawn.

Explanation of Solution

Given:

The points $\left(1,2\right)\text{ and }\left(4,-3\right)$ as solutions but not the point $\left(-2,8\right)$ .

Concept used:

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 a system in equalities that have the points $\left(1,2\right)\text{ and }\left(4,-3\right)$ as solutions but not the point $\left(-2,8\right)$ .

Draw the graph of inequalities that describes the given condition.

The $x$ - coordinates of $\left(1,2\right)\text{ and }\left(4,-3\right)$ are positive and the $x$ - coordinate of a negative. It means the following inequalities will satisfy the given condition.

  $\begin{array}{l}x\ge 0.\\ x\le 5.\end{array}$

Therefore, the system of linear inequalities is:

  $x\ge 0\text{ and }x\le 5.$

Draw the graph of $x\ge 0\text{ and }x\le 5$ as shown below. The intersection of blue and red colors represents the solution set. The point $\left(1,2\right)\text{ and }\left(4,-3\right)$ are in the solution set and the point $\left(-2,8\right)$ is not the solution set.

The graph of the inequalities $x\ge 0\text{ and }x\le 5$ :

Hence, the graph of system of linear inequalities is drawn.