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# What is the value of y in the system above?

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Intern
Joined: 02 Apr 2013
Posts: 4
GMAT 1: 570 Q47 V28
What is the value of y in the system above?  [#permalink]

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03 Apr 2013, 05:15
1
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:00) correct 29% (02:29) wrong based on 169 sessions

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I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1

What is the value of y in the system above?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Math Expert
Joined: 02 Sep 2009
Posts: 52344
Re: What is the value of y in the system above?  [#permalink]

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03 Apr 2013, 05:24
gmatfeelizzle wrote:
I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1

What is the value of y in the system above?

(A) -2
(B) -1
(C) 0
(D) 1
(E) 2

Multiply the second equation by 2: $$2x + 2y - 2z = 0$$ --> $$2x + 2y =2z$$.

From III: $$2x + 2y - z = 1$$ --> $$2z - z = 1$$ --> $$z=1$$.

Subtract II from I: $$(x + 2y + 3)- (x + y - 1) = 2$$ --> $$y=-2$$.

Hope it's clear.
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Intern
Joined: 02 Apr 2013
Posts: 4
GMAT 1: 570 Q47 V28
Re: What is the value of y in the system above?  [#permalink]

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03 Apr 2013, 05:42
is there an easier and quicker way to solve this question than my approach? this one took me around 6 minutes to solve, so i guess there must be an easier way.

my approach:

1. from the given system of equations i can make equation II. to be x + y = z

2. now put that in III. :

2x + 2y - (x + y) = 1

= 2x + 2y - x - y = 1

= x + y = 1

that gives us z = 1!

3. put z = 1 in I. and solve:

x + 2y + 3 = 2; calculate minus 3

= x + 2y = -1; calculate minus x

= 2y = -1 - x;

4. now put 2y = -1 - x in III. and solve:

2x + (-1 - x) - 1 = 1

= x - 2 = 1; calculate plus 2

that gives us x = 3

5. now solve for y with x = 3 and z = 1:

x + y = 1

= 3 + y = 1; calculate minus 3

that gives y = -2, and hence answer (A) -2

any quicker way?
Director
Joined: 23 Jan 2013
Posts: 560
Schools: Cambridge'16
What is the value of y in the system above?  [#permalink]

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05 Aug 2016, 01:51
my solution of

x+2y+3z=2
x+y-z=0
2x+2y-z=1

1. subtract equation#2 from equation#1 because we do not need x, we look for y

y+4z=2

2. to eliminate x in second pair multiply equation#2 by -2 and add equation#2 to equation#3

z=1

3. substitute z with 1 and get y=-2
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Joined: 09 Sep 2013
Posts: 9458
Re: What is the value of y in the system above?  [#permalink]

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18 Jan 2018, 01:54
Hello from the GMAT Club BumpBot!

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Re: What is the value of y in the system above? &nbs [#permalink] 18 Jan 2018, 01:54
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