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

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New post 02 Dec 2019, 01:51
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[GMAT math practice question]

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

A. \((1, 0)\)

B. \((2, 3)\)

C. (\(\frac{1}{2}, \frac{-3}{4}\))

D. (\(\frac{1}{2}, \frac{-3}{2}\))

E. (\(\frac{4}{3}, \frac{-3}{4}\))

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Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =  [#permalink]

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New post 02 Dec 2019, 03:08
MathRevolution wrote:
[GMAT math practice question]

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

A. \((1, 0)\)

B. \((2, 3)\)

C. (\(\frac{1}{2}, \frac{-3}{4}\))

D. (\(\frac{1}{2}, \frac{-3}{2}\))

E. (\(\frac{4}{3}, \frac{-3}{4}\))


Explanation:
Solving Equation: (x-3)/3 = (y+2)/2
2x-6=3y+6
2x-3y=12
Need Above Equation in form of ax + by = 3
(2/4)x + (-3/4)y = 3
(1/2,-3/4)
IMO-C

:please Please give kudos, if you find my explanation Good Enough :please
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 8435
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GPA: 3.82
Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =  [#permalink]

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New post 04 Dec 2019, 02:17
=>

\(\frac{x-3}{3} = \frac{y+2}{2}\)

=> \(2(x - 3) = 3(y + 2)\) (cross multiplying)

=> \(2x - 6 = 3y + 6\) (multiplying through the brackets)

=> \(2x - 3y = 12\) (adding like terms)

=> \((\frac{1}{2})x - (\frac{3}{4})y = 3\) (dividing both sides by \(4\)).

Then we have \(a = \frac{1}{2}\) and \(b = \frac{-3}{4}\).

Therefore, C is the answer.
Answer: C
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Re: For x, y satisfying x-3/3= y+2/2, x and y always satisfies ax + by =   [#permalink] 04 Dec 2019, 02:17
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