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555-605 (Medium)|   Algebra|      
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Bunuel
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If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the 05 Feb 2019, 02:22
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76% (02:10) correct 24% (02:42) wrong based on 164 sessions

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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
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A
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If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the 05 Feb 2019, 02:58
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Re-arranging the terms gives, x(m-n)-y(p-q) = 0
Given p-q = 2
x(m-n) = 2y
y/x = m-n/2
-1/3 = m-n/2
m-n = -2/3
or n-m = 2/3

A is the answer.
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If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the 05 Feb 2019, 03:12
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Bunuel
If \(mx + qy − nx − py = 0\), \(p − q = 2\), and \(y/x = -\frac{1}{3}\), 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
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mx -nx -py +qy = 0

x(m-n) - y(p-q) = 0
x(m-n) = 2y
y/x = (m-n)/2

y/x = -1/3
m-n = -2/3
n-m = 2/3

A
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If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the 24 Jan 2020, 11:14
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Bunuel
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
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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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If mx + qy − nx − py = 0, p − q = 2, and y/x = -1/3, then which of the 22 Aug 2022, 17:29
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