Chapter 3, Problem 18MCQ

To determine

To calculate: The solution set for the system of inequalities with the help of a graph.

  $\begin{array}{c}y\ge 2x-5\\ y\le x+4\end{array}$

Answer to Problem 18MCQ

The solution set for the system of inequalities is Region 3.

  

Explanation of Solution

Given information:

The system of inequalities,

  $\begin{array}{c}y\ge 2x-5\\ y\le x+4\end{array}$

Calculation:

Consider the system of inequalities,

  $\begin{array}{c}y\ge 2x-5\\ y\le x+4\end{array}$

Plot the inequalities $y\ge 2x-5$ and $y\le x+4$ on the coordinate plane.

  

Region 1 and 3 depicts the inequality $y\ge 2x-5$ and region 2 and 3 depicts the inequality $y\le x+4$ .

The region common to both the inequalities is region 3.

Therefore, the solution set of the system of inequalities is region 3.

To verify substitute any arbitrary point say $\left(-10,-10\right)$ from region 3 in the inequalities and check.

For the inequality $y\ge 2x-5$ , substitute x as $-10$ and y as $-10$ .

  $\begin{array}{c}-10\ge 2\left(-10\right)-5\\ -10\ge -20-5\\ -10\ge -25\end{array}$

For the inequality $y\le x+4$ , substitute x as $-10$ and y as $-10$ .

  $\begin{array}{c}-10\le -10+4\\ -10\le -6\end{array}$

Both the inequalities satisfy the point.

Thus, the solution set for the system of inequalities is region 3.