16Hit1600
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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