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Without graphing, classify the system 3x - 2y = 4 and y = (3/2)x - 2.
AOne solution; consistent and independent
BNo solution; inconsistent and independent
CInfinitely many solutions; inconsistent and dependent
DInfinitely many solutions; consistent and dependent
Answer & Solution
Correct answer: D. Infinitely many solutions; consistent and dependent
1. Rewrite the first equation in slope-intercept form: 3x - 2y = 4 becomes y equals three-halves x minus 2.
2. Compare it to the second equation, y equals three-halves x minus 2, and notice they are identical.
3. Since both equations describe the exact same line, the lines are coincident.
4. A system with coincident lines has infinitely many solutions and is classified as consistent and dependent.
_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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