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2017 AMC 12B Problem 3

Problem 3 of 25EasierAlgebra

Suppose that xx and yy are nonzero real numbers such that 3x+yx−3y=−2.\frac{3x + y}{x - 3y} = -2. What is the value of x+3y3x−y?\frac{x + 3y}{3x - y}?

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Solution

The equation gives 3x+y=−2(x−3y)3x + y = -2(x - 3y) =−2x+6y,= -2x + 6y, so 5x=5y,5x = 5y, meaning x=y.x = y. Then x+3y3x−y=y+3y3y−y=4y2y=2.\frac{x + 3y}{3x - y} = \frac{y + 3y}{3y - y} = \frac{4y}{2y} = 2. Thus, the correct answer is D.
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