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# If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the

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Re: If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the [#permalink]
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Bunuel wrote:
If $$mx + qy − nx − py = 0$$, $$p − q = 2$$, and $$\frac{y}{x} = -\frac{1}{3}$$, then which of the following is true?

A. n – m = 2/3

B. n – m = -2/3

C. m + n = 2/3

D. m + n = 3/2

E. m + n = -3/2

Tricky!!!
First notice that we can perform some factoring in parts
We'll start by rearranging the terms to get some like terms together.

Take: $$mx + qy − nx − py = 0$$
Rearrange to get: $$mx − nx + qy − py = 0$$
Factor in parts to get: $$x(m − n) + y(q - p) = 0$$
Now subtract $$y(q - p)$$ from both sides to get: $$x(m − n) = -y(q - p)$$
Rewrite the right side of the equation as follows: $$x(m − n) = y(-q + p)$$
Simplify to get: $$x(m − n) = y(p - q)$$

Divide both sides by $$x$$ to get: $$m − n = \frac{y(p - q)}{x}$$

Rewrite the right side of the equation to get: $$m − n = \frac{y}{x}(p - q)$$

Replace $$p − q$$, and $$\frac{y}{x}$$ to get: $$m − n = -\frac{1}{3}(2)$$

Simplify to get: $$m − n = -\frac{2}{3}$$

Multiply both sides by $$-1$$ to get: $$-m + n = \frac{2}{3}$$

Finally, rewrite as follows: $$n - m = \frac{2}{3}$$

Cheers,
Brent
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Re: If mx + qy nx py = 0, p q = 2, and y/x = -1/3, then which of the [#permalink]
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Re: If mx + qy nx py = 0, p q = 2, and y/x = -1/3, then which of the [#permalink]
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