AlgebraVery hardProduct of the coordinates of an intersection
Algebra practice question
In the xy-plane, the lines 2x + y = 8 and x − 2y = −1 intersect at a single point. What is the product of the coordinates of that point?
Answer: 6
From the second equation x = 2y − 1; substituting, 4y − 2 + y = 8, so y = 2 and x = 3. The product is 6.
Common wrong answers
- If you answered 1
- 1 is x − y.
- If you answered 5
- 5 is the sum of the coordinates.
- If you answered -6
- −6 has the sign of y wrong.
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