ToGraph:The system of linear inequalities
Answer to Problem 15E
The graph of the system of linear inequalities
Explanation of Solution
Given:
The system of linear inequalities
Concept Used:
The graph of asystem of linear inequalities in two variables shows all the solutions of the system.
Calculation:
Given the system of linear inequalities
Consider thelinear inequalities
The corresponding equation
Graphing the equation
Plotting the graph of the equation
Testing a point on either side of the solid line
Consider a coordinate
Substituting the coordinate
Thus,
Shading the half-plane that contains
Plotting the second inequality on the same above graph
Consider thesecond linear inequalities
The corresponding equation
For
For
The points on the equation
Since, in the given inequality
So, plotting the graph of the equation
Testing a point on either side of the dashed line
Consider a coordinate
Substituting the coordinate
Thus,
Shading the half-plane that contains
Plotting the intersection of the two shaded regions, we have
Conclusion:
The graph of the system of linear inequalities
Chapter 5 Solutions
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