Fermat 2024 Part B - Question 18, CEMC UWaterloo

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Difficulty: 5

This problem is tagged with fermat, fermat24, highschool.

(Fermat 2024, Part B, Question 18, CEMC - UWaterloo)

Suppose that $x$ and $y$ are real numbers that satisfy the two equations
$3x+2y=6$
$9x^2+4y^2=468$
What is the value of $xy$?
$(A)$ $-36$
$(B)$ $-12$
$(C)$ $-32$
$(D)$ $-120$
$(E)$ $-32$

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