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

$$x + y - z = 2$$

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

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

Given:
2x + y + z = 3 (1)
5x + 3y + z = 8 (2)

Asked: what is the value of x + y - z?

(2)-2*(1) gives
x+y-z=8-2*3=2

IMO E

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

Plug in numbers x=1, y=1, z=0 which satisfies both equations which is easy to guess.

Therefore, x+y-z = 1+1-0 = 2
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - [#permalink]
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