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If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x

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GreenlightTestPrep
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If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 06:10
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If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x and y?

(A) -5.2
(B) -2.6
(C) -1.3
(D) 1.3
(E) 2.6
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B
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Farina
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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 07:06
Given,
6x - 7y = 11 and -5x - 5y = 13
Add the two equations, we get
x-12y=24
x = 24 + 12y

Put in eq 2:
-5x - 5y = 13
-5 (24+12y) - 5y = 13
-133 = 65 y
y = -2.04

put in other equation for x
x = 24 + 12y
x = 24 + 12(-2.04)
x = -0.55

so x + y = -2.04 - 0.55
= -2.6 (approx) option B
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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 07:25
Nice work, @Farina

Can you find a different (faster) solution?

Cheers,
Brent
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Farina
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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 07:29
GreenlightTestPrep wrote:
Nice work, @Farina

Can you find a different (faster) solution?

Cheers,
Brent


Thanks, yes it took me long to solve. First I tried to multiply equation 1 and 2 by 5 and 6 to balance the equation and to use elimination method but I found that even more longer. So No I am also looking forward to easy solution Sir.
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GreenlightTestPrep
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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 07:34
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GreenlightTestPrep wrote:
If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x and y?

(A) -5.2
(B) -2.6
(C) -1.3
(D) 1.3
(E) 2.6


Given: 6x - 7y = 11 and -5y = 13 + 5x
First things first, let's rearrange the terms in the second equation so that they match up with the terms in the first equation.

Take: -5y = 13 + 5x
Add 5y to both sides of the equation: 0 = 13 + 5x + 5y
Subtract 13 from both sides of the equation: -13 = 5x + 5y
Rewrite as: 5x + 5y = -13

We get:
6x - 7y = 11
5x + 5y = -13

Wait a second!
Notice that the question does NOT ask us to find the individual values of x and y.
We just need to find the value of x + y

We can take 5x + 5y = -13 and factor the left side to get 5(x + y) = -13
So, if we divide both sides of the equation by 5, we get: x + y = -2.6
Bingo!!!

Answer: B

Cheers,
Brent
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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   04 Aug 2020, 08:43
Wow Brent! Thanks a lot

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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink] New post   16 Jul 2023, 11:51
Hello from the GRE Prep Club BumpBot!

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Re: If 6x - 7y = 11 and -5y = 13 + 5x, what is the sum of x [#permalink]
16 Jul 2023, 11:51
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