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

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

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New post Updated on: 30 Jul 2018, 05:08
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A
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D
E

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Question Stats:

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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, 03:45.
Last edited by carcass on 30 Jul 2018, 05:08, edited 1 time in total.
Edited by Carcass
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Re: In the system of equations above, what is the value of x ?  [#permalink]

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New post 16 Jan 2014, 03:45
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: \((4x + y)-(x+y) = 1-(-2)\) --> \(3x=3\) --> \(x=1\).

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

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New post 16 Jan 2014, 10:44
2
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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New post 16 Jan 2014, 23:23
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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New post 17 Jan 2014, 10:26
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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Re: In the system of equations above, what is the value of x ?  [#permalink]

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New post 18 Jan 2014, 06:09
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: \((4x + y)-(x+y) = 1-(-2)\) --> \(3x=3\) --> \(x=1\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: In the system of equations above, what is the value of x ?  [#permalink]

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New post 18 Jan 2014, 13:41
seems sub 500...I haven't taken an official GMAT yet...I hope this is a 550 question :shock: 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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New post 16 Nov 2018, 08:12
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
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Re: In the system of equations above, what is the value of x ? &nbs [#permalink] 16 Nov 2018, 08:12
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