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# If 4x−3y=10 and 7x−8y=34 , what is the value x−y ?

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Posts: 43866
If 4x−3y=10 and 7x−8y=34 , what is the value x−y ? [#permalink]

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01 Mar 2017, 04:41
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Question Stats:

81% (02:03) correct 19% (01:46) wrong based on 99 sessions

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If 4x−3y=10 and 7x−8y=34, what is the value x−y?

A. 2
B. 4
C. 6
D. 8
E. 12
[Reveal] Spoiler: OA

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Joined: 11 Sep 2015
Posts: 2055
Re: If 4x−3y=10 and 7x−8y=34 , what is the value x−y ? [#permalink]

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01 Mar 2017, 04:50
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Bunuel wrote:
If 4x−3y=10 and 7x−8y=34, what is the value x−y?

A. 2
B. 4
C. 6
D. 8
E. 12

Nice question!

The long approach is to solve the system for the INDIVIDUAL values of x and y and then use those values to determine the value of x-y.

The quick approach is to ADD the two equations (4x−3y=10 and 7x−8y=34) to get: 11x - 11y = 44
Then divide both sides by 11 to get: x - y = 4

Cheers,
Brent
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Re: If 4x−3y=10 and 7x−8y=34 , what is the value x−y ? [#permalink]

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01 Mar 2017, 10:44
Bunuel wrote:
If 4x−3y=10 and 7x−8y=34, what is the value x−y?

A. 2
B. 4
C. 6
D. 8
E. 12

$$4x − 3y = 10 ---------------> (I)$$
$$7x − 8y = 34 ---------------> (II)$$

$$11x − 11y = 44$$

Or, $$x − y = 4$$

Thus, answer must be (B) 4
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Re: If 4x−3y=10 and 7x−8y=34 , what is the value x−y ? [#permalink]

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02 Mar 2017, 17:40
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Expert's post
Bunuel wrote:
If 4x−3y=10 and 7x−8y=34, what is the value x−y?

A. 2
B. 4
C. 6
D. 8
E. 12

Adding the two equations together, we have:

4x - 3y = 10

7x - 8y = 34

11x - 11y = 44

Dividing both sides by 11, we have:

x - y = 4

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Re: If 4x−3y=10 and 7x−8y=34 , what is the value x−y ?   [#permalink] 02 Mar 2017, 17:40
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