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# In the system of equations above, what is the value of x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 55732
In the system of equations above, what is the value of x ?  [#permalink]

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Updated on: 30 Jul 2018, 06:08
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:56) correct 10% (01:20) wrong based on 801 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

$$2x +2y =-4$$

$$4x + y = 1$$

In the system of equations above, what is the value of x ?

(A) -3
(B) -1
(C) $$\frac{2}{5}$$
(D) 1
(E) $$1\frac{1}{4}$$

Problem Solving
Question: 41
Category: Algebra Algebra Simultaneous equations
Page: 67
Difficulty: 550

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Originally posted by Bunuel on 16 Jan 2014, 04:45.
Last edited by carcass on 30 Jul 2018, 06:08, edited 1 time in total.
Edited by Carcass
Math Expert
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Posts: 55732
Re: In the system of equations above, what is the value of x ?  [#permalink]

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16 Jan 2014, 04:45
1
1
SOLUTION

2x +2y =-4
4x + y = 1
In the system of equations above, what is the value of x ?

(A) -3
(B) -1
(C) 2/5
(D) 1
(E) $$1\frac{1}{4}$$

Reduce the first equation by 2 and subtract it from the second one: $$(4x + y)-(x+y) = 1-(-2)$$ --> $$3x=3$$ --> $$x=1$$.

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Re: In the system of equations above, what is the value of x ?  [#permalink]

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16 Jan 2014, 11:44
3
We multiply the second equation by 2 and solving the two equations,get x=1 as follows:
2x+2y=-4
8x+2y=2
Reversing signs in second equation
-6x=-6
Hence x=1.
Ans. D

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Re: In the system of equations above, what is the value of x ?  [#permalink]

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17 Jan 2014, 00:23
1
This is probably a sub-500 level question:

Multiply second equation by 2, change the sign and cancel y;
After that x can be determined.

Ans is (D) 1.
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Re: In the system of equations above, what is the value of x ?  [#permalink]

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17 Jan 2014, 11:26
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

2x +2y =-4
4x + y = 1
In the system of equations above, what is the value of x ?

(A) -3
(B) -1
(C) 2/5
(D) 1
(E) $$1\frac{1}{4}$$

4x+y = 1
x+y = -2

Subtracting below equation from first => 3x = 3 => x = 1 - Option D)
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Math Expert
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Posts: 55732
Re: In the system of equations above, what is the value of x ?  [#permalink]

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18 Jan 2014, 07:09
SOLUTION

2x +2y =-4
4x + y = 1
In the system of equations above, what is the value of x ?

(A) -3
(B) -1
(C) 2/5
(D) 1
(E) $$1\frac{1}{4}$$

Reduce the first equation by 2 and subtract it from the second one: $$(4x + y)-(x+y) = 1-(-2)$$ --> $$3x=3$$ --> $$x=1$$.

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Joined: 06 Jan 2014
Posts: 37
Re: In the system of equations above, what is the value of x ?  [#permalink]

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18 Jan 2014, 14:41
seems sub 500...I haven't taken an official GMAT yet...I hope this is a 550 question I need the test to be as easy as possible!

I did it by taking the second equation...creating a "y=" and subbing
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Re: In the system of equations above, what is the value of x ?  [#permalink]

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16 Nov 2018, 09:12
2x + 2y = -4
4x + y = 1

There is a easy method to get the answer in 20 seconds. To determine x, (difference of cross multiply coefficients of y with constants)/(difference of cross multiply coeff. of y with coeff. of x)

x = (2(1)-1(-4))/(2(4)-1(2)) = (2+4)/(8-2) = 6/6 = 1

Similarly we can determine y, (difference of cross multiply coefficients of x with constants)/(difference of cross multiply coeff. of x with coeff. of y)

y = (2(1)-4(-4))/(2(1)-4(2)) = (2-(-16))/(2-8) = (18/-6) = -3
Re: In the system of equations above, what is the value of x ?   [#permalink] 16 Nov 2018, 09:12
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