Chapter 3, Problem 21SGR

To determine

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

  $\begin{array}{c}y<2x-3\\ y\ge 4\end{array}$

Answer to Problem 21SGR

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

  

Explanation of Solution

Given information:

The system of inequalities,

  $\begin{array}{c}y<2x-3\\ y\ge 4\end{array}$

Calculation:

Consider the system of inequalities,

  $\begin{array}{c}y<2x-3\\ y\ge 4\end{array}$

Plot the inequalities $y<2x-3$ and $y\ge 4$ on the coordinate plane.

  

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

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 $y<2x-3$ , substitute x as 10 and y as 10.

  $\begin{array}{c}10<2\left(10\right)-3\\ 10<20-3\\ 10<17\end{array}$

For the inequality $y\ge 4$ , substitute x as 10 and y as 10.

  $10\ge 4$

Both the inequalities satisfy the point.

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