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Is the ordered pair (3, 2) a solution to the system 3x - y = 7 and x - 2y = 4?
AYes, it makes both equations true
BNo, it makes only the first equation true
CNo, it makes only the second equation true
DNo, it makes neither equation true
Answer & Solution
Correct answer: B. No, it makes only the first equation true
1. Substitute x = 3 and y = 2 into 3x - y = 7: 3(3) - 2 equals 9 minus 2, which equals 7, a true statement.
2. Substitute the same values into x - 2y = 4: 3 - 2(2) equals 3 minus 4, which equals -1, not 4, a false statement.
3. Since the pair fails the second equation, it is not a solution to the system, even though it satisfies the first.
_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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