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Solve by elimination: 3x + 4y = 12 and y = 3 - (3/4)x.
AExactly one solution, at the point (0, 3)
BNo solution, since the equations are inconsistent
CExactly one solution, at the point (4, 0)
DInfinitely many solutions, since the equations are dependent
Answer & Solution
Correct answer: D. Infinitely many solutions, since the equations are dependent
1. Write the second equation in standard form: y equals 3 minus three-fourths x becomes three-fourths x plus y equals 3.
2. Clear the fraction by multiplying by 4: 3x plus 4y equals 12, which is identical to the first equation.
3. Multiply this new equation by -1 and add it to the first equation: 0 equals 0, a true statement.
4. Since the result is always true, the equations are consistent but dependent, so the system has infinitely many solutions.
_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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