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For x, y satisfying x-3/3= y+2/2, x and y always satisfies

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by Max@Math Revolution » Mon Dec 02, 2019 12:31 am
[GMAT math practice question]

For x, y satisfying (x-3)/3 = (y+2)/2, x and y always satisfies ax + by = 3. What is ( a, b )?

A. (1, 0)
B. (2, 3)
C. (1/2, -3/4)
D. (1/2, -3/2)
E. (4/3, -3/4)
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by Max@Math Revolution » Wed Dec 04, 2019 12:53 am
=>

(x-3)/3 = (y+2)/2
=> 2(x - 3) = 3(y + 2) (cross multiplying)
=> 2x - 6 = 3y + 6 (multiplying through the brackets)
=> 2x - 3y = 12 (adding like terms)
=> (1/2)x - (3/4)y = 3 (dividing both sides by 4).
Then we have a = 1/2 and b = -3/4.

Therefore, C is the answer.
Answer: C
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