(a)
To prove:
(a)
Explanation of Solution
Proof:
Proof by contradiction: if
Plugging the values into the first equation,
Now
The solution
Conclusion:
Therefore,
(b)
To prove: if the system has two different solutions, then it has infinitely many solutions.
(b)
Explanation of Solution
Proof:
From the above proof, the way to derive new solutions for the given system is seen. Plug the new values found after using the formula back into said formula to find new, and by definition distinct, solutions.
It is continued doing this to no end, (stumbled onto one of Zero's Paradoxes), and found that there can be infinite solutions to the given system.
Conclusion:
Therefore, there can be infinite solutions to the given system.
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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