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In the definition of a linear equation Ax + By = C, why must A and B not both be zero?
ASo that the equation involves at least one variable
BSo that the constant C stays a positive number
CSo that the equation has exactly one solution
DSo that both x and y must always be equal
Answer & Solution
Correct answer: A. So that the equation involves at least one variable
1. If both A and B were zero, the equation would reduce to just 0 = C, with no x or y in it at all.
2. Requiring that A and B are not both zero guarantees the equation genuinely involves at least one of the two variables.
3. The sign of C, the number of solutions, and whether x equals y are separate questions unrelated to this specific requirement.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 4 "Graphs", section 4.1 Use the Rectangular Coordinate System_
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