AlgebraHardTwo unknown parameters from a common point
Algebra practice question
In the xy-plane, the lines y = ax + 2 and y = 3x + b intersect at the point (2, 8), where a and b are constants. What is the value of a + b?
Answer: 5
The point is on both lines: 8 = 2a + 2 gives a = 3, and 8 = 6 + b gives b = 2. So a + b = 5.
Common wrong answers
- If you answered 6
- 6 comes from b = 3, treating b as a slope.
- If you answered 7
- 7 comes from a = 5 (8 = 2a − 2) with a sign slip.
- If you answered 10
- 10 is the sum of the point's coordinates.
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