The given system of equation has to be solved and graphed for its solutions, co-ordinates of all vertices and tells that the set of solution is bounded or not.
Answer to Problem 41E
The set of solution is:
All solutions, or solution set is in the shaded plane so, the solution of the given inequalities is bounded.
Explanation of Solution
Given:
Calculations:
The given eqns. are:
Use the test point
Substitute
For eq. (1):
It does not satisfy the given equation. Need to shade the region on or below the solid line which does not have the point
For eq. (2):
It satisfies the given equation. Clearly, need to shade the region on or below the solid line which have the point
For eq. (3):
It satisfies the given equation.
Clearly, need to shade the region on or below the solid line which does have the point
So, the graph of the given inequality equations is:
Now, the determine the vertex:
Solve first two eqns:
Put
Now,
So, the first vertex point is
Solve two eqns by taking subtraction of (5) and (6):
From eq. (6):
So, the second vertex point is
Solve (4) and (6):
From eq. (6):
Put in eq. (4):
So, the third vertex point is
So, the set of solution is:
All solutions, or solution set is in the shaded plane so, the solution of the given inequalities is bounded.
Conclusion:
Hence, the given set of equations is derived as above.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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