AMC10 2017 B

AMC10 2017 B · Q4

AMC10 2017 B · Q4. It mainly tests Linear equations, Manipulating equations.

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

假设$x$和$y$是非零实数，使得$$\frac{3x + y}{x - 3y} = -2.$$$\frac{x + 3y}{3x - y}$的值是多少？

(A) -3 -3

(B) -1 -1

(D) 2 2

(E) 3 3

Answer

Correct choice: (D)

正确答案：（D）

Solution

The given equation implies that $3x + y = -2(x - 3y)$, which is equivalent to $x = y$. Therefore $$\frac{x + 3y}{3x - y} = \frac{4y}{2y} = 2.$$

给定方程意味着$3x + y = -2(x - 3y)$，等价于$x = y$。因此$$\frac{x + 3y}{3x - y} = \frac{4y}{2y} = 2.$$

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