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Solve by elimination: -6x + 15y = 10 and 2x - 5y = -5.
ANo solution, since the equations are inconsistent
BExactly one solution, at the point (0, 1)
CInfinitely many solutions, since the equations are dependent
DExactly one solution, at the point (5, 3)
Answer & Solution
Correct answer: A. No solution, since the equations are inconsistent
1. Multiply the second equation by 3 to try to eliminate a variable: 6x minus 15y equals -15.
2. Add this to the first equation, -6x plus 15y equals 10: 0 equals -5.
3. Since 0 can never equal -5, this is a false statement.
4. A false result after elimination means the equations are inconsistent, so the system has no solution.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.3 Solve Systems of Equations by Elimination_
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