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Two equations in a system are called dependent when what is true?
AEvery solution of one equation is also a solution of the other
BEach equation has its own separate set of solutions
CNeither equation has any solutions of its own at all
DThe two equations use different variables entirely
Answer & Solution
Correct answer: A. Every solution of one equation is also a solution of the other
1. The definition states that dependent equations share every solution: whatever solves one equation also solves the other.
2. Having a completely separate set of solutions describes independent equations instead, the opposite idea.
3. Having no solutions at all or using different variables are unrelated conditions that do not define dependence.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_
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