Xy = -36

x + y = 9

\( xy = -36 \)

\( \frac{xy}{x} =\frac{-36}{x} \)

\( y = \frac{-36}{x} \)

\( x + y = 9 \)

\( x + \frac{-36}{x} = 9 \)

\( \frac{x^{2}}{x} + \frac{-36}{x} = 9 \)

\( \frac{x^{2} - 36}{x} = 9 \)

\( 9x = x^{2} - 36 \)

\( 0 = x^{2} - 9x - 36 \)

\( x = \frac{-(-9) \± \sqrt{(-9)^{2} - 4(1)(-36)}}{2(1)} \)

\( x = \frac{9 \± \sqrt{81 + 144}}{2} \)

\( x = \frac{9 \± \sqrt{225}}{2} \)

\( x = \frac{9 \± 15}{2} \)

\( x = \frac{9 + 15}{2} \) \( or \) \( x = \frac{9 - 15}{2} \)

\( x = \frac{24}{2} \) \( or \) \( x = \frac{-6}{2} \)

\( x = 12 \) \( or \) \( x = -3 \)

x + y = 9 or x + y = 9

12 + y = 9 or -3 + y = 9

- 12 - 12 + 3 + 3

y = -3 or y = 12

(x, y) = (12,3) or (x, y) = (-3, 12)

The two numbers that add up to 9 and multiply to -36 are the numbers -3 and 12.

What two numbers multiply to get -36 and add to get 9

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