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02 May 2024, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
31% (01:02) correct
69%
(01:08)
wrong
based on 273
sessions
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If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
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05 May 2024, 22:30
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Official Solution:
If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
Given \(c\) and \(b\) are different numbers, then \(c - b \neq 0\), this means \(a*y = c - b = some \ nonzero \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = nonzero \ number\) has no solutions for \(y\).
If \(a \neq 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Therefore, there is either one solution or no solution, depending on the value of \(a\).
Answer: E
If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
Given \(c\) and \(b\) are different numbers, then \(c - b \neq 0\), this means \(a*y = c - b = some \ nonzero \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = nonzero \ number\) has no solutions for \(y\).
If \(a \neq 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Therefore, there is either one solution or no solution, depending on the value of \(a\).
Answer: E
General Discussion
02 May 2024, 07:00
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If a ≠ 0, then y will have only one value.
But, if a = 0 then y can have infinitely many values.
Cannot be determined with given info. Option E
But, if a = 0 then y can have infinitely many values.
Cannot be determined with given info. Option E
