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Without graphing, classify the system y = 3x - 1 and 6x - 2y = 12.
AOne solution; consistent and independent
BNo solution; inconsistent and independent
CInfinitely many solutions; consistent and dependent
DNo solution; consistent and independent
Answer & Solution
Correct answer: B. No solution; inconsistent and independent
1. Rewrite the second equation in slope-intercept form: 6x - 2y = 12 becomes y equals 3x minus 6.
2. Compare slopes and intercepts: both lines have slope 3, but the first has y-intercept -1 and the second has y-intercept -6.
3. Since the slopes match but the intercepts differ, the lines are parallel.
4. A system with parallel lines has no solution and is classified as inconsistent and independent.
_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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