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Chapter 6: Q67. (page 392)

Solve each system of inequalities by graphing.

x>3y<x+2

Short Answer

Expert verified

The solution of the system of inequalities is double shaded region in the graph given below:

Step by step solution

01

Step 1. Graph the inequalities.

Here the equations are:

x>3and y<x+2

The strategy is to solve the inequalities by graphing. The graph of the system of inequalities is drawn as below:

02

Step 2. State interpretation of the graph. 

The graph ofx=3 is dashed (the line in black) and is not included in the graph of the solution. The graph ofy=x+2 (the line in brown) is dashed again and therefore, is not included in the graph of the solution.

03

Step 3. State the conclusion.

The solution of the system is the set of ordered pairs in the intersection of the graphs of x>3andy<x+2. This region is green double shaded region.

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