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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: \(n - m = \frac{2}{3}\)

Answer: A

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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