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Solve by substitution: 5x - 2y = -10 and y = (5/2)x.
AExactly one solution, at the point (-2, -5)
BNo solution, since the equations are inconsistent
CInfinitely many solutions, since the equations are dependent
DExactly one solution, at the point (0, 0)
Answer & Solution
Correct answer: B. No solution, since the equations are inconsistent
1. Substitute five-halves x in place of y in the first equation.
2. 5x minus 2 times five-halves x equals -10, which simplifies to 5x minus 5x equals -10.
3. The variable terms cancel out entirely, leaving the false statement 0 equals -10.
4. Since the result is never true, the equations are inconsistent, and the system has no solution.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.2 Solve Systems of Equations by Substitution_
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