alleryStart learning →What is a consistent system of equations?
AA system of equations with no solution
BA system where every equation has the same slope
CA system with exactly two variables
DA system of equations with at least one solution
Answer & Solution
Correct answer: D. A system of equations with at least one solution
1. The definition states directly that a consistent system has at least one solution.
2. A system with no solution is called inconsistent instead, which is the opposite idea.
3. Sharing a slope describes parallel or coincident lines specifically, and having two variables is just a feature of the system, neither of which defines consistency.
_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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