AlgebraHardTwo constants from a shared point on two lines
Algebra practice question
In the xy-plane, the lines ax + by = 12 and 2ax − by = 6 both pass through the point (2, 1), where a and b are constants. What is the value of b?
Answer: 6
Substitute (2, 1): 2a + b = 12 and 4a − b = 6. Adding: 6a = 18, so a = 3, and then b = 12 − 6 = 6.
Common wrong answers
- If you answered 2
- 2 is the x-coordinate of the point.
- If you answered 3
- 3 is a, not b.
- If you answered 9
- 9 comes from b = 12 − 3, forgetting to double a.
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