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# Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -

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Math Expert
Joined: 02 Sep 2009
Posts: 51285
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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09 Dec 2015, 07:41
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Difficulty:

35% (medium)

Question Stats:

73% (02:00) correct 27% (02:34) wrong based on 195 sessions

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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: GMATQuantum

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CEO
Joined: 11 Sep 2015
Posts: 3243
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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09 Dec 2015, 07:54
2
3
Bunuel wrote:
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

Given: 2x + y + z = 3 and 5x + 3y + z = 8
Take 2x + y + z = 3 and multiply both sides by 2 to get the EQUIVALENT fraction: 4x + 2y + 2z = 6

We now have:
5x + 3y + z = 8
4x + 2y + 2z = 6

Subtract the bottom equation from the top equation to get:
x + y - z = 2

Cheers,
Brent
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##### General Discussion
Manager
Joined: 15 Feb 2015
Posts: 101
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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09 Dec 2015, 09:20
Bunuel wrote:
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: GMATQuantum

A quick one!

Subtract Eq 1 from Eq2 ( both are given)

I got 3x+2y=5 wheni did that.

Again, from this equation, subtract eq1 ( 2x+y+z=3)

The answer is x+y-z=2

Hence E
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Posts: 294
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Concentration: Strategy, General Management
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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09 Dec 2015, 16:05
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

5x + 3y + z = 8
-2(2x + y + z = 3)

which equals x + y - z = 2

E. 2
Intern
Joined: 27 Oct 2015
Posts: 26
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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09 Dec 2015, 17:31
2x + y + z = 3
5x +3y + z = 8

Multiply the first equation by 2 and subtract it from the 2nd equation
x+y-z = 8 - 6 = 2
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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16 Jul 2017, 13:22
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

$$2x + y + z = 3$$ ====> 1

$$5x + 3y + z = 8$$ ====> 2

Multiply Eq. 1 by 2

$$4x + 2y + 2z = 6$$ ===> 3

Substract Eq. 3 from 2

$$5x + 3y + z = 8$$
-$$(4x + 2y + 2z = 6)$$

We Get:

$$x + y - z = 2$$

Hence, Answer is E

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Manager
Joined: 18 Jan 2017
Posts: 129
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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17 Jul 2017, 10:20
Bunuel wrote:
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

Source: GMATQuantum

====

2x + y + z = 3 and 5x + 3y + z = 8
Multiply both sides of 2x + y + z = 3 by 2
to get 4x + 2y + 2z = 6

5x + 3y + z = 8
4x + 2y + 2z = 6
Subtract them to get x + y - z = 2

Hence the answer is E
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Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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20 Jul 2017, 15:37
Bunuel wrote:
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

We can multiply the first equation by -2, and we have:

-4x - 2y - 2z = -6

Adding the above equation with the equation 5x + 3y + z = 8, we have:

x + y - z = 2

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Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - &nbs [#permalink] 08 Aug 2018, 11:24
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# Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -

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