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2017 AMC 10B Problem 4

Problem 4 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

Given that 3x+yx−3y=−2,\frac{3x+y}{x-3y}=-2, we can multiply by the denominator to get 3x+y=6y−2x.3x+y = 6y-2x. Solving, we can see that x=y.x=y. Therefore, x+3y3x−y=x+3x3x−x=2.\frac{x+3y}{3x-y} = \frac{x+3x}{3x-x}=2. Thus, the correct answer is D .
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Tagged: rational equation · algebraic manipulation

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