alleryStart learning →The sum of two numbers is zero. One number is nine less than the other. Find the numbers.
A9.0 and -9.0
B4.5 and 4.5
C9/2 and -9/2
D-9/2 and -9/2
Answer & Solution
Correct answer: C. 9/2 and -9/2
1. Let n be the first number and m be the second number, giving the system n + m = 0 and n = m - 9.
2. Substitute m - 9 for n in the first equation: (m minus 9) plus m equals 0.
3. Simplify: 2m minus 9 equals 0, so 2m equals 9, giving m equals nine-halves.
4. Substitute back to find n equals m minus 9, which is negative nine-halves, so the numbers are 9/2 and -9/2.
_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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