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2024 AMC 12B Question 13

AMC12 · 2024 AMC 12B

Question 13

There are real numbers $x,$ $y,$ $h,$ and $k$ that satisfy the system of equations

$$
x^2 + y^2 - 6x - 8y = h
$$

$$
x^2 + y^2 - 10x + 4y = k.
$$

What is the minimum possible value of $h + k?$
  1. $-54$
  2. $-46$
  3. $-34$
  4. $-16$
  5. $16$