(a)
To graph: the given equations.
(a)
Answer to Problem 1ST
Explanation of Solution
Given:
Calculation:
Since the given system consists of a linear and a quadratic equation, it is a quadratic system. The real solutions of such a system can be determined by finding the points at which the individual graphs intersect.
Let us graph the two given equations on the same co-ordinate plane, and find the number of points at which they intersect.
Conclusion:
(b)
the number of real solutions.
(b)
Answer to Problem 1ST
The system of equations has 4 real solutions.
Explanation of Solution
Calculation:
From the graph, it can be seen that the graphs intersect at four points. So, the system of equations has 4 real solutions.
Conclusion:
The system of equations has 4 real solutions.
(c)
To estimate: each real solution to the nearest half-unit.
(c)
Answer to Problem 1ST
Therefore, the four real solutions of the given system are
Explanation of Solution
Calculation:
The four points where the graphs intersect are approximately
Therefore, the four real solutions of the given system are
Conclusion:
Therefore, the four real solutions of the given system are
Chapter 9 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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