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How many rules are needed at the very least before a system in two unknowns can have a single solution?
AOne rule is enough if it holds both unknowns
BAt least as many rules as there are unknowns
CAlways three rules, one more than the unknowns
DAny number of rules will give one solution
Answer & Solution
Correct answer: B. At least as many rules as there are unknowns
1. A single rule in two unknowns is satisfied by every point along a whole line, so it pins down nothing on its own.
2. A second rule is needed to cut that line down to a single point.
3. In general there must be at least as many rules as there are unknowns.
4. Even that does not guarantee one answer, since two rules may give a parallel pair or the same line twice.
5. So option B states the requirement correctly while option A stops one rule short.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_
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