Chapter D, Problem 1E

To determine

To graph:

The solutions for the provided system of linear inequalities.

Answer to Problem 1E

Solution:

The solutions of the system is the region contained in the graphs of both inequalities.

Explanation of Solution

Given:

The provided system of linear inequalities is $\{\begin{array}{l}y\ge x+1\\ y\ge 3-x\end{array}$

Procedure:

Graphing the solutions of a system of linear inequalities:

Step 1: Graph each inequality in the system on the same set of axes.

Step 2: The solutions of the system are the points common to the graphs of all the inequalities in the system.

Calculation:

Consider the inequalities $y\ge x+1$, $y\ge 3-x$

Graph both the inequalities on the same set of axes.

Since both the inequality symbols are $\ge$, the boundary lines are also included in the solution.

The solutions of the system are the regions shown by the darkest shading in the graph below.

Graph:

Therefore, the solutions of the system is the region contained in the graphs of both inequalities.