AlgebraVery hardProduct of an intersection point's coordinates
Algebra practice question
In the xy-plane, the lines 3x + 2y = 12 and x = 2y intersect at a single point. What is the product of the x- and y-coordinates of that point?
Answer: 4.5 or 9/2
Substituting x = 2y gives 8y = 12, so y = 1.5 and x = 3; the product is 4.5.
Common wrong answers
- If you answered 3
- 3 is x alone.
- If you answered 4
- 4 uses x = 2 and y = 2, which does not satisfy 3x + 2y = 12.
- If you answered 1.5
- 1.5 is y alone.
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