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Working through a system by substitution leaves the statement 9 = 13. What does that ending mean?
AThe system is dependent with endless solutions
BThe two unknowns are equal to 9 and to 13
CThe solution is the pair made from 9 and 13
DThe system is inconsistent and has no solution
Answer & Solution
Correct answer: D. The system is inconsistent and has no solution
1. The statement 9 = 13 is false for every possible pair of values.
2. Reaching a false statement by correct working means the starting assumption cannot hold.
3. The assumption was that some pair satisfies both rules, so no such pair exists.
4. A system with no solution is inconsistent, and its lines are parallel.
5. Options B and C read the two numbers as answers, but they are the two sides of a contradiction rather than values of unknowns.
6. Option A belongs to the other ending, an identity such as 0 = 0.
_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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