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If 2/x + 3/y = 9/xy and 4/x + 9/y = 21/xy, where x ≠ 0 and y ≠ 0, then what is the value of x + y?

Multiplying both equations by \(xy\) gives \(3x + 2y = 9\) and \(9x + 4y = 21\). Solving this linear system yields \(x = 1\) and \(y = 3\), so \(x + y = 1 + 3 = 4\).

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If 2/x + 3/y = 9/xy and 4/x + 9/y = 21/xy, where x ≠ 0 and y ≠ 0, then what is the value of x + y?

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Correct answer C

Multiplying both equations by xyxy gives 3x+2y=93x + 2y = 9 and 9x+4y=219x + 4y = 21. Solving this linear system yields x=1x = 1 and y=3y = 3, so x+y=1+3=4x + y = 1 + 3 = 4.

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