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GRE Prep Club Team Member
Joined: 20 Feb 2017
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If 2x + y = 7 and x – y = 2, then x + y = (A) 6
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01 Jan 2020, 04:03
01 Jan 2020, 04:03
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If \(2x + y = 7\) and \(x – y = 2\), then \(x + y =?\)
(A) 6
(B) 4
(C) \(\frac{3}{2}\)
(D) 0
(E) –5
(A) 6
(B) 4
(C) \(\frac{3}{2}\)
(D) 0
(E) –5
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
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Concentration: General Management
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GMAT 1: 700 Q51 V31
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Re: If 2x + y = 7 and x – y = 2, then x + y = (A) 6
[#permalink]
02 Jan 2020, 09:11
02 Jan 2020, 09:11
There are two general ways of solving simultaneous equations
Method 1: Substitution
Take value of one of the variable from one equation and substitute in other to get an equation in terms of only one variable
2x + y = 7 => y = 7-2x
Substitute this value of y in second equation
x - y =2
=> x - (7-2x) = 2
=> x - 7 + 2x = 2 => 3x = 2+7 = 9 => x=3
Substitute value of x in any of the equations and get value of y
using equation 2
x-y = 2 => 3 - y = 2 => y = 1
So, x+y = 3+1 = 4
Method 2: Elimination of one Variable
Multiple one or both of those equations by a positive or a negative integer to eliminate one of the variables
In the given equation we just need to add the two equations to eliminate y, as coefficient of y is +! in one case and -1 in other
2x + y = 7
x - y = 2
Adding we get
3x + y-y = 7+2 = 9
=> x=3
and rest is same as previous method.
So, Answer is B.
Hope it helps!
Method 1: Substitution
Take value of one of the variable from one equation and substitute in other to get an equation in terms of only one variable
2x + y = 7 => y = 7-2x
Substitute this value of y in second equation
x - y =2
=> x - (7-2x) = 2
=> x - 7 + 2x = 2 => 3x = 2+7 = 9 => x=3
Substitute value of x in any of the equations and get value of y
using equation 2
x-y = 2 => 3 - y = 2 => y = 1
So, x+y = 3+1 = 4
Method 2: Elimination of one Variable
Multiple one or both of those equations by a positive or a negative integer to eliminate one of the variables
In the given equation we just need to add the two equations to eliminate y, as coefficient of y is +! in one case and -1 in other
2x + y = 7
x - y = 2
Adding we get
3x + y-y = 7+2 = 9
=> x=3
and rest is same as previous method.
So, Answer is B.
Hope it helps!
gmatclubot
Re: If 2x + y = 7 and x – y = 2, then x + y = (A) 6 [#permalink]
02 Jan 2020, 09:11
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