AlgebraVery hardConstants from a known solution
Algebra practice question
The ordered pair (2, −1) is the solution to the system ax + y = 5 and x + by = 5, where a and b are constants. What is the value of a + b?
Answer: 0
Substitute x = 2, y = −1. First equation: 2a − 1 = 5, so a = 3. Second: 2 − b = 5, so b = −3. a + b = 0.
Common wrong answers
- If you answered 3
- 3 is a alone.
- If you answered 6
- 6 uses b = 3, missing the sign: 2 + b(−1) = 5 gives −b = 3, b = −3.
- If you answered -3
- −3 is b alone.
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